if $\displaystyle f(x)= \sum_{k=0}^{\infty} (cos^2x)^k$, then $\displaystyle f(\frac{\pi}{4})$ is

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- Apr 14th 2010, 08:44 PMyoman360series problem
if $\displaystyle f(x)= \sum_{k=0}^{\infty} (cos^2x)^k$, then $\displaystyle f(\frac{\pi}{4})$ is

- Apr 14th 2010, 08:50 PMmaddas
$\displaystyle \cos^2(\frac\pi4) = \frac12$.

- Apr 14th 2010, 11:22 PMHallsofIvy
So this is simply the geometric sum $\displaystyle \sum_{k=0}^\infty \left(\frac{1}{2}\right)^2$