Prove that #sum_(k=1)^n 1/(sin2^kx)=cot x - cot 2^nx# for every #x ne (kpi)/2^k, x in RR, n in NN^+#?
2 Answers
Dec 1, 2016
Not for this sum but for a similar one. Please see explanation.
Explanation:
I get a similar result for
using
I admit that I don't get any idea, for solving the given problem.
Dec 1, 2016
See below.
Explanation:
Always is worth to read Ramanujan's Third Notebook.
With the identity
so we can build a telescopic series such that
summing up we get