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 ▸Let r and s be integers. Then ( 6^(r+s) x 12^(r-s) ) / ( 8^(r) x 9^(r+2s) ) is an integer when: (a) r+s <= 0, (b) s <= 0, (c) r <= 0, (d) r >= s.
When is the inequality x^4 < 8x^2 + 9 true?
Can you please help with Question 5 on the 2008 MAT?
Let a and b be positive real numbers. If x^2 + y^2<=1 then what is the largest that ax+by can get?