Find given that
but ans is
You have taken, .
This is incorrect (substitute n=2 and the right hand side becomes undefined).
Much easier is to treat the summation without breaking it apart into two pieces.
You have to evaluate,
When r=1;
When r=2;
When r=3;
.
.
.
.
.
.
When r=n-1;
When r=n;
Adding all these together you will get the correct answer.