I’m interesting to see the opinion of MO about my question which I posted here in SE, Answers I received have not convinced me, And no clear proof posted there only numerical computation are provided. I should post the question as it is in order to know more about convergence of the titled sequence

Question:

let us moving to telescopic sum using exponent, Assume we have this sequence: an=(1−12)(12−13)...(1n−1n+1) with n≥1, this sequence can be written as power of sequences: xnyncn⋯ such that all them value are in (0,1), I want to know if the titled sequence should converge to 1? and how we can evaluate it for n go to ∞?

**Answer**

**Attribution***Source : Link , Question Author : Zeraouli Rafik , Answer Author : Community*