You are Here: Home >< Maths

# Further Pure 2 - Proof by Induction watch

1. The question says "Express 1/(r+2)r! in the form A/(r+1)! + B/(r+2)! "

I basically would like to know how to get to the line r+1 = A(r+2) + B

Many Thanks
2. (Original post by mathewnutt)
The question says "Express 1/(r+2)r! in the form A/(r+1)! + B/(r+2)! "

I basically would like to know how to get to the line r+1 = A(r+2) + B

Many Thanks
partial fractions

(r + 2 )! = (r + 2) x ( r + 1)!
3. But surely doing partial fractions you would get:

A/(r+2) + B/r! ?

Apologies, This topic massively confuses me
4. (Original post by mathewnutt)
The question says "Express 1/(r+2)r! in the form A/(r+1)! + B/(r+2)! "

I basically would like to know how to get to the line r+1 = A(r+2) + B

Many Thanks
multiplying every term by (r+2)! will get you to that line

for factorial questions write out a few terms first if you dont understand what to do
5. (Original post by mathewnutt)
The question says "Express 1/(r+2)r! in the form A/(r+1)! + B/(r+2)! "

I basically would like to know how to get to the line r+1 = A(r+2) + B

Many Thanks

So

Now multiply both sides by and make use of the fact that

6. (Original post by mathewnutt)
The question says "Express 1/(r+2)r! in the form A/(r+1)! + B/(r+2)! "

I basically would like to know how to get to the line r+1 = A(r+2) + B

Many Thanks
Alternatively:

Now multiply both sides by , to get:

Now, the LHS becomes and the RHS simplifies as in my previous post.
7. Okay, I think i understand now, much better explained than my teachers haha, Many Thanks
8. (Original post by mathewnutt)
Okay, I think i understand now, much better explained than my teachers haha, Many Thanks
No problem.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 8, 2016
Today on TSR

### My dream is to become a WAG

I wont settle for anything else!

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams