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Value of this sum

GROUPS:
I wanted to evaluate the following sum psi(2n+1)/(2n+1)-psi(2n)/(2n) where n ranges from 1 to infinity and psi is the Chebyshev second function. So I wrote the following code.

Sum[ Sum[Floor[Log[Prime[k], 2x+1]] Log[Prime[k]]/(2x+1), {k, 1, PrimePi[2x+1]}]- Sum[Floor[Log[Prime[k], 2x]] Log[Prime[k]]/(2x), {k, 1, PrimePi[2x]}]] ,1]


But it didn't show the answer. Can anybody tell me the answer?
POSTED BY: narayansurya999
Answer
1 year ago
Hi. There appears to be some characters missing from your code. As it is right now, the code doesn't work and is missing the range for the outer summation. 

If Mathematica doesn't return a result, then this often means that a symbolic value for the sum doesn't exist. Are you certain that a symbolic value exists? If not, you may want to use NSum to try finding a numeric estimation. 
POSTED BY: Sean Clarke
Answer
1 year ago