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Prove the following by induction 1ini32nn+122n+12nn3.pdf

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This mathematical statement can be proven by induction. The base case for n=1 is true as both sides equal 1. Assuming the statement holds for n=k, it also holds for n=k+1 by applying the inductive hypothesis and algebraic manipulations. Therefore, by mathematical induction, the statement is true for all positive integers n.

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Prove the following by induction: 1ini3=(2n(n+1))22n+12n,n3

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