# Need help balancing an Induction Proof

• Mar 24th 2010, 12:36 PM
math61688
Need help balancing an Induction Proof
(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
• Mar 24th 2010, 01:20 PM
tonio
Quote:

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

The right side must be $\frac{k+1}{(k+1)+1}=\frac{k+1}{k+2}$ , but then:

$\frac{k}{k+1}+\frac{1}{(k+1)(k+2)}=\frac{1}{k+1}\l eft(k+\frac{1}{k+2}\right)=\frac{1}{k+1}\left(\fra c{k^2+2k+1}{k+2}\right)$ $=\frac{1}{k+1}\cdot \frac{(k+1)^2}{k+2}=\frac{k+1}{k+2}$

Tonio

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

.
• Apr 24th 2010, 09:24 AM
math61688
thanks for the help!