concrete maths, sums. The upper limit does not match the definite sum

Question

In this image

Why is the first term in right side of the equation $a_n b_n$ and not $a_{n-1} b_{n-1}$. Since $k$'s max value is n-1 and not n, as per the described limits on k.

For reference, 2.56 is

Answer 1

the maximal value for $k$ is $n-1$ but you have an index $k+1$. So plug in $n-1$ for $k$ and you obtain $k+1=n-1+1=n$.