Answer
See proof
Work Step by Step
In Problem 98, we proved:
$u_{n+1}=\dfrac{(n+1)(n+2)}{2}$
Compute $u_{n+1}+u_n$ using the formula:
$u_{n+1}+u_n=\dfrac{(n+1)(n+2)}{2}+\dfrac{n(n+1)}{2}$
$=\dfrac{n+1}{2}(n+2+n)$
$=\dfrac{(n+1)(2n+2)}{2}$
$=\dfrac{2(n+1)(n+1)}{2}$
$=(n+1)^2$
We proved:
$u_{n+1}+u_n=(n+1)^2$
