Question

Evaluate:

Answer 1

\[\sum_{n =1}^{\infty}( 1/2^{n})\tan(a/2^{n})\]

Answer 2

a is not = kpi

Answer 3

For n big enough
\[
\left|\tan\left(\frac a {2^n} \right)\right|<1
\]
Your series is abolurtly bounded above by convergent geometric series. So it does converge. There is no way you can compute its sum in closed from. Its numerical approximation is 0.357907 if a=1