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Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 /(i+1)$. Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.
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