Can someone show me algebraically how ((1/2)(n -1) n + 1) + n = (1/2)n(n + 1) + 1

That's pretty much it. According to a book I'm reading, ((1/2)(n -1) n + 1) + n = (1/2)n(n + 1) + 1. The book uses this as a premise that is supposed to be already understood in order to teach something more complicated, but for some reason I'm not getting that answer when I do the algebra. I must be making a mistake somewhere.

Can someone please show me?

Thanks.

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

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

( (n^2)/2 - n/2 + 1 + n )

(n^2)/2 + n/2 + 1

(1/2) ( n^2 + n) +1

(1/2) ( n (n +1)) + 1