Chapter 5.4, Problem 2ES

Evaluate.

(a) ${\displaystyle \underset{k=1}{\overset{4}{\sum }}k\sin \frac{k\pi }{2}}$

(b) ${\displaystyle \underset{j=0}{\overset{5}{\sum }}{\left(-1\right)}^j}$

(c) ${\displaystyle \underset{i=7}{\overset{20}{\sum }}{\pi }^2}$

(d) ${\displaystyle \underset{m=3}{\overset{5}{\sum }}{2}^{m+1}}$

(e) ${\displaystyle \underset{n=1}{\overset{6}{\sum }}\sqrt{n}}$

(f) ${\displaystyle \underset{k=0}{\overset{10}{\sum }}\cos k\pi }$