1. ## Using PMI help!

Hi all,

Well I went to my teacher to get help, but his method just did not work (no idea why). I'm trying to solve this:

For all n in N (where N is the set of natural numbers)$\displaystyle , 1/2(5) + 1/5(8) + ... + 1/(3n-1)(3n+2) = n/6n+4$

I understand the steps to PMI, but when I get to the Inductive Step $\displaystyle P(k+1)$ and try to solve the equality I get completely stuck.

I don't know what I am doing wrong, whether it be the PMI steps or otherwise. Thanks guys.

2. Originally Posted by teacast
Hi all,

Well I went to my teacher to get help, but his method just did not work (no idea why). I'm trying to solve this:

For all n in N (where N is the set of natural numbers)$\displaystyle , 1/2(5) + 1/5(8) + ... + 1/(3n-1)(3n+2) = n/6n+4$

I understand the steps to PMI, but when I get to the Inductive Step $\displaystyle P(k+1)$ and try to solve the equality I get completely stuck.

I don't know what I am doing wrong, whether it be the PMI steps or otherwise. Thanks guys.
for the P(k+1) you must have:

1/2(5) +1/5(8)+.......................+1/(3n-1)(3n+2) + 1/(3n+2)(3n+5) =

=(n+1)/6[(n+1)+4]= (n+1)/2(3n+5)........................................... ............................1

IF (1) is satisfied then the P(k+1) step is satisfied.

Since you already have : 1/2(5) +....................+1/(3n-1)(3n+2)= n/(6n+4) ,substitute that into (1) and you get:

n/(6n+4) + 1/(3n+2)(3n+5) = (n+1)/2(3n+5) or:

n/2(3n+2) + 1/(3n+2)(3n+5) = (n+1)/2(3n+5).

DO THE calculations and you will see that the equation is satisfied