Math Help - how do i show this is a consistent estimator?

1. how do i show this is a consistent estimator?

I have shown that the expected value of $\delta (x)$ is $\theta+1$

How possibly can $\delta (x)$ be an consistent estimator?

Thanks!

casper

2. $P\left(\left|\hat\theta-\theta\right|>\epsilon\right)= {1\over n} \to 0$

while $E\left(\hat\theta-\theta\right)^2=(n)^2{1\over n}+0\left(1-{1\over n}\right)=n\to \infty$