Need help with calculating this sum: $\sum_{n=0}^\infty\frac{1}{2^n}\tan\frac{1}{2^n}$

Question

I need help with calculating this sum: $$\sum_{n=0}^\infty\frac{1}{2^n}\tan\frac{1}{2^n}$$

This is a very good problem. Can you tell me whether you get this from? Thank you. — TCL, May 13 '13 at 01:25

score 17 · Answer 1 · answered May 12 '13 at 21:15

17

Hint: use the fact that $\cot{x}-2\cot{2 x}=\tan{x}$

answered May 12 '13 at 21:15

Ron Gordon

1

Nice. Very Nice. – mick May 12 '13 at 22:30
Awesome result and another trick for my toolbox :) +1 – Chinny84 Jan 07 '15 at 08:30

score 1 · Answer 2 · answered Jan 07 '15 at 08:13

1

i just was reading this book yesterday krishna book

answered Jan 07 '15 at 08:13

Williams Bravo

2 Answers2