Saturday, March 7, 2015

3/7/15

Find the sum from n = 1 to infinity of phi(n)/n^3.  You can use the following facts.  pi^2 / 6 = sum from n = 1 to infinity of 1/n^2, and the sum from n = 1 to infinity of 1/n^3 = a. (Note: phi(n) is the number of integers below n and above one that satisfy gcd(n,k) = 1)

Hint: Start with a given, and work it out till you get the desired expression.

Level: 6

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