Who Says Summation is Easy

Calculus Level 5

Evaluate ∑ m = 1 ∞ ∑ n = 1 ∞ 64 m 2 n 3 m ( n 3 m + m 3 n ) \large\sum_{m=1}^{\infty} \sum_{n=1}^{\infty} \dfrac{64m^{2}n}{3^{m}(n3^{m}+m3^{n})}


The answer is 18.

Shubhendra Singh by Shubhendra Singh , 20, India

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1 solution

Prakhar Bindal
Jun 2, 2016

Interchange m and n and add the two sequences to get an AGP

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you post a detailed solution so that others who can't solve this problem can learn from it?

Calvin Lin Staff - 4 years, 5 months ago

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