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sequence
Recent questions tagged sequence
30
views
1
answers
Define a Cauchy sequence and state its importance in real analysis.
Define a Cauchy sequence and state its importance in real analysis.
MathsGee
Platinum
113k
points
MathsGee
asked
Apr 8
Mathematics
define
cauchy
sequence
real
analysis
+
–
103
views
1
answers
Is there a sequence of polynomials $P_n$ such that:
Is there a sequence of polynomials $P_n$ such that:$$\lim_{n\to\infty} P_n(z) = \begin{cases} 1 & \text{ if } \Im(z) 0 \\ 0 & \text{ if } \Im(z) = 0 \\ -1 & \text{ ...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
sequence
polynomials
approximation
infinity
+
–
149
views
1
answers
Is there a sequence of polynomials $P_n$ such that $P_n(0) = 1$ for all $n$, but $P_n(z) \to 0$ as $n \to \infty$?
Is there a sequence of polynomials $P_n$ such that $P_n(0) = 1$ for all $n$, but $P_n(z) \to 0$ as $n \to \infty$?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
sequence
polynomials
infinity
approximation
formula
+
–
101
views
1
answers
Let $L_1, L_2$ be lines in the plane. For which pairs of $L_1, L_2$ do there exists real functions,
Let $L_1, L_2$ be lines in the plane. For which pairs of $L_1, L_2$ do there exists real functions, harmonic on the entire plane, 0 on $L_1 \cup L_2$, but not vanishing i...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
real
prove
points
region
harmonic
sequence
+
–
75
views
1
answers
Prove that $f_n$ converges uniformly on compact subsets of $\Omega$.
Let $\Omega$ be a region, and $f_n \in \mathcal{H}(\Omega)$ for all $n$. Set $u_n = \Re(f_n)$, and suppose $u_n$ converges uniformly on compact subsets of $\Omega$ and th...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
set
function
sequence
bounded
converge
open
+
–
87
views
1
answers
Let $u,v$ be real harmonic functions on a plane region $\Omega$. Under what conditions is $uv$ harmonic?
Let $u,v$ be real harmonic functions on a plane region $\Omega$. Under what conditions is $uv$ harmonic?Further, show that $u^2$ may not be harmonic on $\Omega$, unless $...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
points
region
harmonic
real
prove
sequence
+
–
67
views
1
answers
Compute $$\int_0^\infty \frac{dx}{1 + x^n}$$ for $n \geq 2$.
Compute$$\int_0^\infty \frac{dx}{1 + x^n}$$for $n \geq 2$.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
sequence
real
proof
analysis
approximation
epsilon
function
+
–
119
views
1
answers
The solution of the inequality \(3(2-x) \geq 2(1-x)\) for real \(x\) is
(1) The solution of the inequality \( 3(2-x) \geq 2(1-x) \) for real \( x \) is
A.M9
111
points
A.M9
asked
Feb 26
Mathematics
prove
real
sequence
analysis
inequality
+
–
97
views
1
answers
Solution \( e^{i \pi}+1=0 \)
Solution \( e^{i \pi}+1=0 \)
S.A9
114
points
S.A9
asked
Feb 24
Mathematics
equation
prove
sequence
function
set
euler
+
–
94
views
1
answers
Explain \( e^{i \pi}+1=0 \)
Explain \( e^{i \pi}+1=0 \)
S.A9
114
points
S.A9
asked
Feb 24
Mathematics
equation
prove
sequence
euler
function
beautiful
set
+
–
68
views
1
answers
Let \( \left\{f_{i}\right\} \) be a uniform Cauchy sequence consisting of uniformly continuous functions on a closed, bounded interval \( I \). Show that the limit is uniformly continuous.
Let \( \left\{f_{i}\right\} \) be a uniform Cauchy sequence consisting of uniformly continuous functions on a closed, bounded interval \( I \). Show that the limit is uni...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
sequence
cauchy
triangle
inequality
set
prove
converge
+
–
123
views
1
answers
Show that for any \( 0<a<1 \) the sequence \( \left\{x^{i}\right\} \) converges uniformly to 0 on \( [0, a] \), but not for \( a=1 \).
Show that for any \( 0<a<1 \) the sequence \( \left\{x^{i}\right\} \) converges uniformly to 0 on \( [0, a] \), but not for \( a=1 \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
prove
converge
uniformly
sequence
set
construct
sequences
+
–
83
views
1
answers
Show that a sequence that converges cannot have two limits.
Show that a sequence that converges cannot have two limits.
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
show
sequence
converges
limits
+
–
102
views
1
answers
Show that a sequence that converges is a Cauchy sequence. Hint: write \( \xi_{i}-\xi_{j}=\left(\xi_{i}-\xi\right)+\left(\xi-\xi_{j}\right) \) and use the triangle inequality.
Show that a sequence that converges is a Cauchy sequence. Hint: write \( \xi_{i}-\xi_{j}=\left(\xi_{i}-\xi\right)+\left(\xi-\xi_{j}\right) \) and use the triangle inequal...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
sequence
cauchy
triangle
inequality
+
–
104
views
2
answers
The HCF of the two numbers is 29 and their sum is 174. What are the numbers?
The HCF of the two numbers is 29 and their sum is 174. What are the numbers?
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 15
Mathematics
numbers
product
hcf
lcm
first
sequence
formula
+
–
122
views
1
answers
Why is a graph of a sequence discrete?
Why is graph of sequence discrete?
Th1391
103
points
Th1391
asked
Feb 14
Mathematics
graph
of
sequence
discreet
+
–
76
views
1
answers
Evaluate \( e^{i \pi}+1=0 \)
Evaluate \( e^{i \pi}+1=0 \)
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 14
Ask Me Anything
equation
prove
sequence
+
–
92
views
1
answers
What is the arithmetic mean?
What is the arithmetic mean?
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 31
AI & Data Science
arithmetic
mean
sequence
calculate
+
–
75
views
1
answers
What is the palindrome of 66?
What is the palindrome of 66?
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 26
Mathematics
numbers
calculate
sequence
sum
arithmetic
value
palindrome
+
–
164
views
1
answers
What is arithmetic geometry?
What is arithmetic geometry?
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 31, 2023
Mathematics
geometry
congruence
sequence
algebraic
expression
arithmetic
+
–
131
views
1
answers
What role do incentive schemes play in OOM?
What role do incentive schemes play in OOM?
MathsGee
Platinum
113k
points
MathsGee
asked
Nov 24, 2023
Business & Entrepreneurship
play
role
sequence
affect
+
–
155
views
1
answers
Determine the common difference for the sequence.
Given a sequence of numbers:\[2 ;-7 ;-16 ;-25 ;-34 ; \ldots\]Determine the common difference for the sequence (if there is one).
MathsGee
Platinum
113k
points
MathsGee
asked
Nov 20, 2023
Mathematics
sequence
calculate
numbers
sequences
complete
grade12
data
+
–
156
views
1
answers
Determine the common difference for the sequence (if there is one).
Given a sequence of numbers:\[-2 ; 2 ;-11 ;-8 ;-13 ; \ldots\]Determine the common difference for the sequence (if there is one).
MathsGee
Platinum
113k
points
MathsGee
asked
Nov 20, 2023
Mathematics
sequence
calculate
numbers
grade12
sequences
complete
+
–
276
views
1
answers
How do I show that all terms in a pattern are even?
How do I show that all terms in a pattern are even?
MathsGee
Platinum
113k
points
MathsGee
asked
Nov 14, 2023
Mathematics
sequence
sequences
prove
converge
+
–
237
views
1
answers
Consider the following quadratic number pattern: \( 6 ; 10 ; 18 ; \ldots \ldots \)
Consider the following quadratic number pattern: \( 6 ; 10 ; 18 ; \ldots \ldots \)1. Write down the following two terms of the pattern.2. Determine the equation of the ge...
MathsGee
Platinum
113k
points
MathsGee
asked
Oct 19, 2023
Mathematics
sequence
calculate
pattern
sum
questions
sequences
quadratic
+
–
401
views
1
answers
What is the impact of creatine on cognition?
What is the impact of creatine on cognition?
MathsGee
Platinum
113k
points
MathsGee
asked
Aug 16, 2023
Health & Wellness
impact
cognition
creatine
sequence
affect
behavior
advertising
+
–
203
views
2
answers
Evaluate \(9^{\frac{ 150}{300}}\)
Evaluate \(9^{\frac{ 150}{300}}\)
Edzai Zvobwo
Bronze Status
6.2k
points
Edzai Zvobwo
asked
Jul 16, 2023
Mathematics
calculate
sequence
sum
arithmetic
series
terms
general
+
–
152
views
1
answers
In what sequence do cognition, affect, and behavior play a role in advertising?
In what sequence do cognition, affect, and behavior play a role in advertising?
MathsGee
Platinum
113k
points
MathsGee
asked
Jun 22, 2023
Advertising & Marketing
sequence
cognition
affect
behavior
advertising
+
–
594
views
2
answers
Prove that \(n^2=(n+1)(n-1)+1\)
Prove that \(n^2=(n+1)(n-1)+1\)
MathsGee
Platinum
113k
points
MathsGee
asked
Jun 14, 2023
Mathematics
prove
real
function
sequence
set
vector
convexity
+
–
322
views
1
answers
Explain \( e^{i \pi}+1=0 \)
Explain \( e^{i \pi}+1=0 \)
MathsGee
Platinum
113k
points
MathsGee
asked
May 14, 2023
Mathematics
equation
prove
sequence
euler
beautiful
+
–
172
views
1
answers
Find the nth term of the quadratic sequence 2, 6, 12, 20, 30, ...
Find the nth term of the quadratic sequence 2, 6, 12, 20, 30, ...
MathsGee
Platinum
113k
points
MathsGee
asked
May 8, 2023
Mathematics
sequence
calculate
formula
pattern
numbers
patterns
behaviour
+
–
251
views
0
answers
Here are the first 5 terms of a sequence.
Here are the first 5 terms of a sequence. \[\begin{array}{lllll}29 & 25 & 21 & 17 & 13\end{array}\]Find an expression, in terms of \(n\), for the \(n\)th term of this seq...
MathsGee
Platinum
113k
points
MathsGee
asked
Apr 16, 2023
Mathematics
sequence
calculate
questions
terms
formula
+
–
273
views
1
answers
1.1 The following pattern is given: 7:3:-1: (2) 1.1.1 1.1.2 (2) Find the general term (7) of the pattern in the form T, = dn+c. Which term of the pattern will be equal to -237?
Grade 11 quetions
MANUEL-MAKGETHA
103
points
MANUEL-MAKGETHA
asked
Mar 29, 2023
Mathematics
number
pattern
sequence
quadratic
+
–
412
views
1
answers
Who discovered pi?
Who discovered pi?
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Mar 13, 2023
Mathematics
prove
equation
sequence
sum
euler
beautiful
pi
+
–
295
views
1
answers
Who discovered this equation \( e^{i \pi}+1=0 \)?
Who discovered this equation \( e^{i \pi}+1=0 \)?
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 17, 2023
Mathematics
equation
euler
most
beautiful
prove
sum
sequence
+
–
520
views
1
answers
What is a geometric sequence?
What is a geometric sequence?
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Feb 10, 2023
Mathematics
definition
geometric
sequence
+
–
533
views
1
answers
What are axioms of arithmetic?
What are axioms of arithmetic?
AstraNova
Diamond
67.9k
points
AstraNova
asked
Feb 6, 2023
Mathematics
axioms
sequence
arithmetic
+
–
613
views
1
answers
What is geometric thinking ?
What is geometric thinking ?
AstraNova
Diamond
67.9k
points
AstraNova
asked
Feb 6, 2023
Mathematics
calculate
sequence
grade12
geometric
arithmetic
prove
series
+
–
317
views
1
answers
\(8 ; 24 ; 72 ; \ldots \ldots\)
\(8 ; 24 ; 72 ; \ldots \ldots\)a) Write down the next 3 terms of the sequence.b) Find the general term.c) Show by calculation whether 5832 is a term of this sequence or n...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 30, 2023
Mathematics
sequence
sum
calculate
arithmetic
general
terms
series
+
–
210
views
1
answers
Given the number pattern \(50 ; 47 ; 44\);
Given the number pattern \(50 ; 47 ; 44\);a) Determine the nth term of this pattern.b) Determine which term of the pattern is equal to \(-67\).c) Calculate the number of ...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 30, 2023
Mathematics
series
sequence
number
pattern
+
–
611
views
1
answers
What is a Cauchy-Riemann equation?
What is a Cauchy-Riemann equation?
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 27, 2023
Mathematics
prove
riemann
function
interval
integrable
lebesgue
sequence
+
–
282
views
1
answers
Evaluate the trig expression
Evaluate:(1) \(\dfrac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{\tan 225^{\circ} \cdot \cos 200^{\circ}}\) (2) \(\dfrac{\sin 36^{\circ}}{\sin 12^{\circ}}-\dfrac{\cos 36^{\ci...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 24, 2023
Mathematics
equation
sine
identity
expression
cosine
prove
sequence
+
–
410
views
0
answers
In an arithmetic sequence \(S_n=n^2-2 n\). Use your formula in 2 to determine the value of:
In an arithmetic sequence \(S_n=n^2-2 n\). Use your formula in 2 to determine the value of:(a) \(\mathrm{T}_7\)(b) \(\mathrm{T}_{50}\)(c) \(\mathrm{T}_n\)
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
sequence
calculate
general
terms
sum
value
prove
+
–
455
views
0
answers
Consider the geometric sequence: \(\quad 8 x^2 ; 4 x^3 ; 2 x^4 ; \ldots \ldots \ldots\)
Consider the geometric sequence: \(\quad 8 x^2 ; 4 x^3 ; 2 x^4 ; \ldots \ldots \ldots\)(a) Show that the general term is given by \(\mathrm{T}_n=2^{4-n} \cdot x^{1+n}\)(b...
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
arithmetic
sum
calculate
sequence
terms
general
value
+
–
441
views
0
answers
What is the greatest value of \(p\) for which the series \(\sum_{k=1}^p 10(3)^{k-1}<2300\) ?
What is the greatest value of \(p\) for which the series \(\sum_{k=1}^p 10(3)^{k-1}<2300\) ?
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
series
converge
sum
infinite
sequence
equation
grade12
+
–
358
views
0
answers
Calculate the difference between \(S_{\infty}\) and \(S_7\) of \(4+\frac{4}{3}+\frac{4}{9}+\ldots\)
Calculate the difference between \(S_{\infty}\) and \(S_7\) of \(4+\frac{4}{3}+\frac{4}{9}+\ldots\)
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
series
calculate
sequence
sum
terms
general
arithmetic
+
–
440
views
0
answers
The 3rd and 12th terms of an arithmetic progression are 12 and \(-24\) respectively. Determine the 49th term.
The 3rd and 12th terms of an arithmetic progression are 12 and \(-24\) respectively. Determine the 49th term.
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
sequence
grade12
calculate
arithmetic
questions
equations
unknown
+
–
524
views
0
answers
The 11th term of an arithmetic sequence is 32 and the sum of the first 11 terms is 187 . Calculate the 21st term.
The 11th term of an arithmetic sequence is 32 and the sum of the first 11 terms is 187 . Calculate the 21st term.
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
sequence
grade12
calculate
arithmetic
questions
geometric
people
+
–
491
views
0
answers
\(2 ; x ; y\) are the first three terms of an arithmetic sequence. If the 2nd term is decreased by 1 , the three terms will form a geometric sequence. Calculate \(x\) and \(y\).
\(2 ; x ; y\) are the first three terms of an arithmetic sequence. If the 2nd term is decreased by 1 , the three terms will form a geometric sequence. Calculate \(x\) and...
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
sequence
grade12
calculate
questions
arithmetic
geometric
people
+
–
319
views
0
answers
Calculate \(n\) if \(\quad \sum_{k=1}^n(3 k+1)=650\)
Calculate \(n\) if \(\quad \sum_{k=1}^n(3 k+1)=650\)
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
series
infinite
sequence
function
convergent
value
divergent
+
–
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