I´m trying to learn something about matematical induction. This chapter starts with sums (Sigma)

There is this easy problem I do not understand.

It says calculate the Sigma: from k=1;to n. where

The textbook answer says: Answer:

But when I do it I get:

starts at k=1 so I get:

Now I try to evaluate the last term:

/multiply by n(n+1)

=

that gives me

so I get

Now to evaluate the sum I take the (first term +last term)multiply by n and devide by 2.

That gives me =

clearly Iám doing someting very very stupid...anyone got an idéa whats wrong here?