I am working on the following problem,
I have managed to first prove that the series is convergent, using the conditions for the alternating series test, although am unsure how to find the exact sum. I have attempted a method similar to telescoping series although this did not work. A previous part of the exercise was to find the following.
I am wondering if it is possible to use this result to prove the sum of the first series is ln(2/3), or if there is a method of calculating the sum i am unaware of. I am aware of the alternating series approximation however this questions asks to prove the exact value so i do not think it is applicable. Am i missing something major?