FP2 doubt

In the Edexcel book, on page 15 ( the answer to Example 4 , part b ) why is it written as 1/2 + 1/3 instead of the general terms 1/(n-1) and 1/n ?

thanks for any help! :biggrin:

bump

bump

How about writing out the problem so that the large amount of people here without that textbook know what your question is?

Reply 4

princejan7

Example 4

a. Express 2/(r+1)(r+3) in partial fractions
b. Hence prove by method of differences that

n
Sigma 2/(r+1)(r+3) = n(an+b)/6(n+2)(n+3)
r=1

Reply 5

Dragon

I don't know the method of differences so I can't really help you on part (b). If the answer has no

n

's in it, I assume it's because they will all cancel out or something.

Reply 6

Piecewise

Method of differences = Telescoping.

Original post by princejan7

In the Edexcel book, on page 15 ( the answer to Example 4 , part b ) why is it written as 1/2 + 1/3 instead of the general terms 1/(n-1) and 1/n ?

I'm not sure what you mean. The question looks OK to me. Start by writing:

\displaystyle \sum_{r=1}^{n}\frac{2}{(r+1)(r+3)} = \sum_{r=1}^{n}\frac{(r+3)-(r+1)}{(r+1)(r+3)} = \cdots

then try telescoping it.

Reply 7

princejan7

Original post by Piecewise

Method of differences = Telescoping.
I'm not sure what you mean. The question looks OK to me. Start by writing:

\displaystyle \sum_{r=1}^{n}\frac{2}{(r+1)(r+3)} = \sum_{r=1}^{n}\frac{(r+3)-(r+1)}{(r+1)(r+3)} = \cdots

then try telescoping it.

Im assuming you have the book with you...

At part b after using method of differences up till r = 3, a (1/2), (1/3), - (1/n+2) and
-(1/n+3) are left over.
Why isn't the (1/2) and (1/3) written as (1/n-1) and (1/n)?

Thanks!