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    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
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    (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)!
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    But surely doing partial fractions you would get:

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

    Apologies, This topic massively confuses me
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    (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
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    (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
    \displaystyle \frac{1}{(r+2)r!} = \frac{1}{(r+2)r!} \times \frac{r+1}{r+1} = \frac{r+1}{(r+2)(r+1)r!} = \frac{r+1}{(r+2)!}

    So \displaystyle \frac{r+1}{(r+2)!} = \frac{A}{(r+1)!} + \frac{B}{(r+2)!}

    Now multiply both sides by (r+2)! and make use of the fact that

    \displaystyle \frac{(r+1)!}{(r+2)!} = \frac{(r+1)!}{(r+2)(r+1)!} = \frac{1}{r+2}
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    (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:

    \displaystyle \frac{1}{(r+2)r!} = \frac{A}{(r+1)!} + \frac{B}{(r+2)!}

    Now multiply both sides by (r+2)!, to get:

    \displaystyle \frac{(r+2)!}{(r+2)r!} = \frac{A(r+2)!}{(r+1)!} = \frac{B(r+2)!}{(r+2)!}

    Now, the LHS becomes \frac{(r+2)(r+1)r!}{(r+2)r!} = r+1 and the RHS simplifies as in my previous post.
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    Okay, I think i understand now, much better explained than my teachers haha, Many Thanks
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    (Original post by mathewnutt)
    Okay, I think i understand now, much better explained than my teachers haha, Many Thanks
    No problem.
 
 
 
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