Question

Find the sum of integers which are divisible by $2$ from $11$ to $50$

Answer 1

Digits divisible by $2$ from $11$ to $50$ are
$12,14,\mathrm{16.......................},48,50$
we can write its sum as
$\Rightarrow 2(6+7+\mathrm{8.....................}+24+25)$
$=2(S_{25}-S_5)$
where $S_n$ represents Sum of first $n$ integers which is
$=\frac{n(n+1)}{2}$
$\Rightarrow 2(6+7+\mathrm{8.....................}+24+25)$
$=2(\frac{25\times 26}{2}-\frac{5\times 6}{2})=2\times (325-15)=2\times 310=620$