- #1

msell2

- 15

- 0

## Homework Statement

Prove the following sequence {a

_{n}} converges to L=1/2

a

_{n}= n

^{2}/(2n

^{2}+n-1)

## The Attempt at a Solution

Given ε>0 we can determine an N∈

**N**so that |a

_{n}- L|<ε for n≥N. We have:

|a

_{n}-L|=|(n

^{2}/(2n

^{2}+n-1)-(1/2)|

= |(-n+1)/(2(2n-1)(n+1))|

I'm not sure what to do once I get to this point. Any help would be great!