I am trying to learn inductive proofs for a test tomorrow. I am trying to understand a solution for a problem in a book, but my math is a bit rusty. Can somebody explain how these are all equal? I don't understand how the last equation was found from the first equation.
n(n+1)/2 + (n+1) = n(n+1) + 2(n+1)/2 = (n+1)(n+2)/2
factor the numerator.
(n^2 + n + 2n + 2)/2
= (n^2 + 3n + 2)/2
= ((n+1)(n+2))/2