I have to find the formula for the nth partial sum of this series in order to determine if the series converges or diverges. Here's the equation:


What I did so far:

I made it into a single fraction:


Then I split it up into partial fractions:




and so I got the two equations:

$$n(A+B)=-n$$ $$A=n+1$$

Does this look right so far? I know I'd have to use the Elimination method in order to find the sum.

  • $\begingroup$ what is the partial sum for $n$ up to $2?$ What about up to $3?$ $\endgroup$
    – Will Jagy
    Oct 10, 2018 at 0:06
  • $\begingroup$ Please don't make it into one fraction. Just add it as two fractions. Then it's pretty! $\endgroup$ Oct 10, 2018 at 0:07
  • $\begingroup$ it's called "telescopic" for a reason. I have a feeling that a lot of fractions will cancel each other out and you'll only have the first and the last one left $\endgroup$
    – Vasili
    Oct 10, 2018 at 0:12
  • $\begingroup$ Take a step back from the board: obviously $A=B=1$, that's where you started from. $\endgroup$ Oct 10, 2018 at 0:17

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