# Thread: Need Help Balancing Induction Problem

1. ## Need Help Balancing Induction Problem

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

I just need to make the left side equal to the right side. This is what I have:

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

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

2. Originally Posted by math61688
(k/k+1)+ (1/(k+1)(k+2)) = (k+1)/(k+1)+1

I just need to make the left side equal to the right side. This is what I have:

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

k(k+2)+1/(k+1)(k+2) = (k+1)/(k+1)+1
Well the top line in the left hand side of your last equation is...

$k(k+2) + 1 = k^2 + 2k + 1 = (k+1)^2$

So you get

$\frac{(k(k+2)+1)}{(k+1)(k+2)} = \frac{(k+1)^2}{(k+1)(k+2)} = \frac{k+1}{k+2}$.

Which if you want to write it the way you've been doing is...

$\frac{k+1}{(k+1) + 1}$