0

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

danb
  • 55
  • 2
  • 10
  • it means that each expression is equal. they are showing you how they came up with the final expression. try it yourself with paper and pencil, take the left-most expression and find the sum. – Nikola Oct 23 '13 at 04:11
  • When I do the first sum, I get (n^2 + n + 2n + 2)/2 – danb Oct 23 '13 at 04:22
  • 1
    @dan no need to multiply all. it's waste of time. make sence like http://stackoverflow.com/questions/19532588/algebra-help-on-inductive-proof/19532804#19532804 – KarSho Oct 23 '13 at 04:38

2 Answers2

0

factor the numerator. 

  (n^2 + n + 2n + 2)/2
= (n^2 + 3n + 2)/2
= ((n+1)(n+2))/2
Nikola
  • 817
  • 13
  • 19
0

First One is,

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

Got it?

that final /2 is common for both.

KarSho
  • 5,699
  • 13
  • 45
  • 78