Question

What is the value of the expression 172,000 338,650 515,100 1,015,050

Answer 1

$\displaystyle\sum_{i=1}^z~i^2\implies \cfrac{z(z+1)(2z+1)}{6} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\sum_{n=1}^{100}~(3+n^2)\implies \begin{array}{llll} \displaystyle \sum_{n=1}^{100}~3~~ &+& ~~\displaystyle \sum_{n=1}^{100}~n^2\\\\\\ (100)(3)&+&\cfrac{100(100+1)( ~~ 2(100)+1 ~~ )}{6} \\\\\\ 300&+&\cfrac{100(101)(201)}{6} \\\\\\ 300&+&338350 \\\\\\ &&\textit{\LARGE 338650} \end{array}$

Answer 2

The correct answer is 338,650