Why does sum(1/n) diverge but sum(1/n^2) converge?
Sum(1/n) is shown to converge by bracketing the series correctly and then comparing it with a series we know diverges. Sum(1/n^2) can be shown to converge via the integral test (using y=1/x^2), where the integral will be bigger than the series.
Related MAT University answers
All answers ▸How many 0's are at the end of 100! (100 factorial)?
[based on MAT 2018 (G)] The curves y = x^2 + c and y^2 = x touch at a single point. Find c.
Deduce a formula (in terms of n) for the following sum: sum (2^i * i) where 1<=i<=n, n,i: natural numbers ( one can write this sum as: 1*2^1+ 2*2^2+ .. +n*2^n)
How do you solve hard integration questions using information you know