Question

Find the sum $S$ defined by $S={\sum }_{n=1}^{10}(2n+\frac{1}{2})$

Answer 1

$S={\sum }_{n=1}^{10}(2n+\frac{1}{2})$

$=2{\sum }_{n=1}^{10}n+{\sum }_{n=1}^{10}\frac{1}{2}$

$=2.[\frac{n(n+1)}{2}{]}_{n=10}+\frac{1}{2}[n{]}_{n=10}$

$=2.\frac{10.11}{2}+\frac{10}{2}$

$=110+5$

$=115$ (Ans $\to$ 115)