User:Michael Hardy/show-or-hide

Algebra will now establish that

${\frac {n(n+1)}{2}}+(n+1)={\frac {(n+1)((n+1)+1)}{2}}\,,$

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${\begin{aligned}{\frac {n(n+1)}{2}}+(n+1)&=(n+1)\left({\frac {n}{2}}+1\right)\\&=(n+1)\left({\frac {n}{2}}+{\frac {2}{2}}\right)\\&=(n+1)\left({\frac {n+2}{2}}\right)\\&={\frac {(n+1)(n+2)}{2}}\\&={\frac {(n+1)((n+1)+1)}{2}}.\end{aligned}}$

thereby showing that indeed P(n + 1) holds.