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Using the principle of mathematical induction prove that `1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1)` for all `n in N`

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To prove the statement \[ 1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \cdots + \frac{1}{1+2+3+\cdots+n} = \frac{2n}{n+1} \] for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps: ...
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