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How to solve double summations?

Hi everyone!

Can anyone tell me how to solve problems of double summation?

What are tricks to solve them? For instance how to solve this problem:

\[\sum_{ω=1}^{\infty}\sum_{n=1}^{\infty}\frac{ω^{2}n}{3^{n}(n(3^{ω})+ω(3^{n}))}\] Also help with generalised methods .

Note by Shivam Jadhav
9 months, 2 weeks ago

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Not every double sum has a closed form, just as not every single summation has a closed form. Many summation solutions are ad hoc. Jake Lai · 9 months, 2 weeks ago

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@Jake Lai What is ad hoc? Can you explain me general properties to solve double summation using an example? Shivam Jadhav · 9 months, 2 weeks ago

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@Shivam Jadhav "Ad hoc" is a term used to describe methods/solutions that are non-generalizable and applicable to a particular case. Prasun Biswas · 9 months, 2 weeks ago

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