Jacob B.

asked • 02/01/18

How to do the following algebra step in mathematical induction

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

1 Expert Answer


Jacob B.

Multiply (k +2) to the top and the bottom? Then collect terms?


Edward A.

Yup that’s right, multiply top and bottom of first term. once you do that, what is the numerator of the combined left hand side? It’s the same as the numerator of the right hand side.
by the way, I assume the right hand side denominator has an equals sign that MUST be a typographical error, must be k+2.


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