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 Oct 12 awarded Nice Question Oct 8 comment Proving the number of permutations $A,B\;$ with $n+1$ total cycles and $AB=(123\cdots n)$ is $C_n$ Counting in two different ways or giving a bijection between two sets one of which is counted by the LHS and the other is counted by the RHS. Oct 8 asked Proving the number of permutations $A,B\;$ with $n+1$ total cycles and $AB=(123\cdots n)$ is $C_n$ Sep 7 awarded Supporter Sep 6 comment Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ @ Steven Standnicki, I am sorry , I had tried this but this is not working. Sep 6 revised Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ added 1 characters in body Sep 6 comment Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ @Steven Stadnicki . I have edited the question now. Finite calculus is analogous to simple calculus just applied on discrete sets. Here we are working with integers. We might be able to derive the equation using it. Sep 6 revised Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ deleted 3 characters in body Sep 6 awarded Editor Sep 6 revised Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ deleted 21 characters in body Sep 6 asked Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ Sep 3 comment Example of a sequence I had tried this. But couldn't come up with the proper answer. Sep 3 comment Example of a sequence Thanks a lot for your help :) Sep 3 comment Example of a sequence @mixedmath , Thanks a lot for your advise. I will keep this in mind :) Sep 3 awarded Scholar Sep 3 accepted Example of a sequence Sep 3 awarded Student Sep 3 asked Example of a sequence