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in this video we are going to calculate the sum of logarithms of n cubed minus 1 all divided by n q plus 1 add from n equals 2 to infinity before we move on dont forget to give a like subscribe to my channel and turn on post notifications we can show that this series indeed converges with the integral test but im just going to omit it because thats not the main thing that i would like to share about the summation so to evaluate this sum im going to rewrite that as the summation with the same starting and ending points of the logarithm of n cubed minus 1 minus the logarithm of n cubed plus 1. so just splitting the numerator and the denominator then i can factorize n cube minus 1 and n cubed plus 1. so for the first logarithm ill split it as the sum of logs of n minus 1 and n squared plus n plus 1 while for the second logarithm it will become log of n plus 1 and log of n squared minus n plus 1 is simply factorization next im going to split into two summations one dealing with the
