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Mental math - The sum of the first $50$ positive odd integers is $50^2$. Find the sum of the first $50$ positive even integers.

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    There are $50$ kids lined up, you give them $1$ candy, $3$, $5$, and so on. Total candies $50^2$. Now you give each kid one more.2012-12-16

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You are given that $1 + 3 + 5 + \cdots + 99 = 50^2$ You need to compute $2 + 4 + 6 + \cdots + 100$ Note that \begin{align} 2 + 4 + 6 + \cdots + 100 & = (1+1) + (3+1) + (5+1) + \cdots + (99+1)\\ & = (1 + 3 + 5 + \cdots + 99) + (\underbrace{1 + 1 + 1 + \cdots + 1}_{50 \text{ times}})\\ & = 50^2 + 50 \end{align}