F.4 limit questions

1. lim n>infinity (1+2+3+..+n)/n^2
Why we can't treat as 1/n^2+ 2/n^2+..+1/n and then equal 0?

2. lim n>infinity (1+1/2+1/4+...+1/2^n)

3. lim x>infinity ( (x^3+x)^1/3 - (x^3+3)^1/3 )