integral test, after you let you will get a p-integral.
You can prove that converges whenever p exceeds one.
Now we need to be careul where we start this series, that's why I left out the n=2....
I only proved it converged.
To estimate the error, well I guess you should split the sum into two parts.
One from 2 to N and the other from N+1 to infinity.
You can then bound that second sum (which is the remainder via the integral)
.
Call this
You want a bound on .
And you can play the same game with the boxes and use the integral
, solve for N, giving me (b).
The you can sum up to that point.