1. The problem statement, all variables and given/known data Thank you very much for helping me. I have to convert the following summation of a term from 1 to ∞ to a definite integral. Sum for k=1 to ∞: (2+Cosh[2k/x]) Csch^4 [k/x] I have already tried the rules for converting from different sources and websites, which is replace r/n by x repalce1/n by dx replace Ʃ by ∫ but when i plot both the summation and the obtained integral, both are not same. Please tell me where i am doing wrong. Limit n->∞: Sum for k=1 to n: (2+Cosh[2k n/(x n)]) Csch^4 [k n/(x n)] (n/n) Since i cannot take "1/n" common, i multiplied and divided by "n". 1/n->dΔ k/n->Δ it becomes, ∫ (2+Cosh[2Δn/x]) Csch^4 [Δn/x] dΔ limit: 1/n to 1 It will converge for n~10, so we don't have to use "n->∞" and so the solution will not diverge. The Integral obtained is x Coth[1/x] Csch[1/x]^2 - x Coth[n/x] Csch[n/x]^2 When i plot both, the above solution after integration and the actual sum are not the same. Please help me solving this. I am also including the mathematica file along with this post.