2011-04-07, 02:35 AM
1. an = 1/n^2 + 2/n^2 + ... + n/n^2
Ask yourself: what is
sum (i = 1 to n) { i }
That is, the series 1, 2, ..., n.
The denominators are all the same, so you just add up the numerators.
Comes to n(n+1)/2
So a_n = [n(n+1)/2]/n^2
a_n = (n+1) / (2n)
Which pretty clearly diverges, as it's greater than 1/2 for all n.
Ask yourself: what is
sum (i = 1 to n) { i }
That is, the series 1, 2, ..., n.
The denominators are all the same, so you just add up the numerators.
Comes to n(n+1)/2
So a_n = [n(n+1)/2]/n^2
a_n = (n+1) / (2n)
Which pretty clearly diverges, as it's greater than 1/2 for all n.