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 do you differentiate ln(f(x))? Tricks like these occur commonly in STEP questions (including one I was looking at earlier today).
Let a and b be positive integers such that a+b = 20. What is the maximum value that (a^2)b can take?
When is the inequality x^4 < 8x^2 + 9 true?
How many 0's are at the end of 100! (100 factorial)?