How to do the following algebra step in mathematical induction

Question

I am doing an induction proof and they skipped over an algebra step.

 

how does:                            become:

k      +  1                              k(k+2) +1

----      ------------                 --------------

k+1     (k+1)(k+2)               (k+1)(k=2)

 

The original induction problem is:

Summation from 1 to n of:

1         =   n

-----         ----

i(i+1)        n+1

Answer 1

Jacob, you must be overthinking this, because it’s something you learned months ago.The left hand side has the sum of two terms. What is the common denominator of the left hand side? What do you have to do to the terms to put them both over that denominator?