Write down in full the sum of each of the following series , and hence find its value .

(1) $\displaystyle \sum^{5}_{r=1}\frac{90}{r}$

(2) $\displaystyle \sum^{8}_{r=1}\sin\frac{r\pi}{3}$

(3) $\displaystyle \sum^{5}_{r=0}(-1)^r(1+2^{r+1})$

My thought process :

(1) $\displaystyle 90\sum^{5}_{r=1}\frac{1}{r}$

$\displaystyle =90\frac{2}{n(n+1)}$

$\displaystyle =90\frac{2}{5(6)}$

=6 ---- my ans is wrong .

I have no idea how to do the rest .