## Multivariable Calculus, 7th Edition

The series is convergent with a sum $\frac{cos1}{1-cos1}$.
$\Sigma^{\infty}_{k=1} (cos 1)^{k} = \Sigma^{\infty}_{k=1} (cos 1)(cos 1)^{k-1}$ It is a geometric series with $r=cos1$ and $a=cos1$ Since $|r|=|cos1| \lt 1$, the series is convergent and has a sum $\Sigma^{\infty}_{k=1} (cos 1)^{k} = \frac{a}{1-r}$ $= \frac{cos1}{1-cos1}$ $\approx 1.175343$