Let's sum differently

Algebra Level 4

$\large1 + 2^2 + 3 + 4^2 + \cdots + 99 + 100^2 = \, ?$

The answer is 174200.

1 solution

Chew-Seong Cheong
Jul 20, 2016

$\begin{aligned} S & = 1 + 2^2 + 3 + 4^2 + \cdots + 99 + 100^2 \\ & = 1+ 3 + 5+ \cdots + 99 + 2^2 + 4^2 + 6^2 + \cdots + 100^2 \\ & = 1+ 3 + 5+ \cdots + 99 + 2^2 \left(1 + 2^2 + 3^2 + \cdots + 50^2 \right) \\ & = \frac {50(1+99)}2 + 4 \left( \frac {50(51)(101)}6 \right) \\ & = 2500 + 171700 \\ & = \boxed{174200} \end{aligned}$

Ah! Nice solution! I did it the not-so-smart way and used calculator. I used sigma for the squares of even numbers.

Rico Lee - 4 years, 10 months ago

Let's sum differently

The answer is 174200.

1 solution

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