Question

Find the sum $S$ defined by $\sum _{n=1}^{20}(3n-\frac{1}{2})$

Answer 1

$S={\sum }_{n=1}^{20}(3n-\frac{1}{2})$

$=3{\sum }_{n=1}^{20}n-{\sum }_{n=1}^{20}\frac{1}{2}$

$=3.[\frac{n(n+1)}{2}{]}_{n=20}-\frac{1}{2}[n{]}_{n=20}$

$=3.\frac{20.21}{2}-\frac{20}{2}$

$=630-10$

$=620$ (Ans $\to$ 620)