(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given the identity [tex]\frac{2}{(r+1)(r+3)} \equiv \frac{1}{r+1} - \frac{1}{r+3}[/tex]

prove that

[tex] \sum^{n}_{r = 1} \frac{2}{(r+1)(r+3)} = \frac{n(an + b)}{6(n+2)(n+3)}[/tex]

where a and b are constants to be found

2. Relevant equations

3. The attempt at a solution

I subed in number r = 1,2,3,n

r =1: 1/2 - 1/4

r=2:1/3 - 1/5

r= 3: 1/4-1/6

r = n: 1/(n+1) - 1/(n+3)

the ones in red being the ones that dont cancel... so i add them but i get 5n-9/6(n+3)

is there somthing else i need to do?

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# Method of differences exam question

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