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$$ (k+1)[k/2 + 1] = [(k+1)(k+2)] / 2 $$

can anyone explain why the factorization becomes $$ [(k+1)(k+2)] / 2 $$

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I don't understand the question: why there is suddenly an equality sign in the middle of an expression? –  Fabian May 6 '11 at 7:02

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up vote 3 down vote accepted

Answer to the revised question. Observe that the factor $\frac{k}{2}+1=\frac{k+2}{2}$ and the other one is the same on both sides.

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I assume $k=2$ is a typo for $k+2$, and trust you to work out why $(k/2)+1=(k+2)/2$.

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Hi all, I am revising on induction and this is part of the equation it factorize to. $$ 1 + 2 + 3 + ... + k + (k + 1) = [k(k + 1)/2] + (k + 1) $$ $$ = (k + 1) [k / 2 + 1] = (k + 1)(k + 2) / 2 $$ –  optimus May 6 '11 at 7:22
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@liangteh: $k/2+1=\frac{k+2}{2}$. –  Américo Tavares May 6 '11 at 7:25

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