First,

a = (1 + 2 + 3 + ... + n) / (n^2)

When I try to find the limit of a when n tends to infinity,

I have tried two ways:

1. I converted a to

2 - [(1 / 2) ^ (n) ] and get the value 2.

2. I make it to

a = 1 / n^2 + 2 / n^2 + 3 / n^2 + ... + n/ n^2 and then take the limit.

but this give an answer 0.

Why? I know there must be something wrong.