## Calculus (3rd Edition)

(a) -1 (b) $\frac{13}{12}$ (c) $\frac{13}{3}$
(a) $$\sum_{j=3}^{4}\sin(j\frac{\pi}{2})=\sin(3\frac{\pi}{2})+\sin(4\frac{\pi}{2})=\sin(\frac{3\pi}{2})+\sin 2\pi=-1+0=-1$$ (b) $$\sum_{k=3}^{5}\frac{1}{k-1}=\frac{1}{3-1}+\frac{1}{4-1}+\frac{1}{5-1}=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{13}{12}$$ (c) $$\sum_{j=0}^{2}3^{j-1}=3^{0-1}+3^{1-1}+3^{2-1}=3^{-1}+3^{0}+3^{1}=\frac{1}{3}+1+3=\frac{13}{3}$$