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    Hi, as part of a proof through induction question, I have (k+1)(k+1)!, the answer for which is given as 1+(k+1)!, could anyone please explain why this is the case?
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    Could you elaborate a bit more, because what you have described is super vague...
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    (Original post by Star-girl)
    Could you elaborate a bit more, because what you have described is super vague...
    Ok, sorry for the confusion: (k+1)(k+1)!= 1+(k+1)! but how is that the case
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    (Original post by bojbtij)
    Ok, sorry for the confusion: (k+1)(k+1)!= 1+(k+1)! but how is that the case
    It isn't.

    Would you mind posting the whole question?
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    I would but I have no idea how to use sigma notation on here

    (Original post by Star-girl)
    It isn't.

    Would you mind posting the whole question?
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    (Original post by bojbtij)
    I would but I have no idea how to use sigma notation on here
    http://www.thestudentroom.co.uk/wiki/LaTex
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    Prove through induction that \displaystyle\sum_{r=1}^n r*r! =(n+1)!-1
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    Sorry forgot to quote
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    (Original post by bojbtij)
    Prove through induction that \displaystyle\sum_{r=1}^n r*r! =(n+1)!-1
    If you add the (k+1)th term to the right hand side (subbing n for k) then can you go from there?
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    (Original post by bojbtij)
    Prove through induction that \displaystyle\sum_{r=1}^n r*r! =(n+1)!-1
    OK. So what have you done so far? Work me through and we can maybe see where you might have gone wrong.
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    Yes thank you both, a bit of an issue going from (k+1)!(k+2)-1 to (k+2)!-1 though

    (Original post by Wunderbarr)
    If you add the (k+1)th term to the right hand side (subbing n for k) then can you go from there?
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    (Original post by Star-girl)
    OK. So what have you done so far? Work me through and we can maybe see where you might have gone wrong.

    All is well up until the last step i.e. (k+1)!(k+2)-1 to (k+2)!-1
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    (Original post by bojbtij)
    Yes thank you both, a bit of an issue going from (k+1)!(k+2)-1 to (k+2)!-1 though
    What is the definition of n!?
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    n*(n-1)*(n-2)...*3*2*1?

    (Original post by 16Characters....)
    What is the definition of n!?
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    (Original post by bojbtij)
    n+(n-1)+(n-2)+...+3+2+1?
    Not quite,  n! = n(n-1)(n-2)...1 . So multiplication not addition.
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    (Original post by 16Characters....)
    What is the definition of n!?
    Oh right, got it, thank you!
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    (Original post by 16Characters....)
    Not quite,  n! = n(n-1)(n-2)...1 . So multiplication not addition.
    Yeah sorry, bit of a lapse
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    (Original post by bojbtij)
    All is well up until the last step i.e. (k+1)!(k+2)-1 to (k+2)!-1
    (k+1)!=?
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    (Original post by bojbtij)
    Yes thank you both, a bit of an issue going from (k+1)!(k+2)-1 to (k+2)!-1 though
    You haven't done anything wrong - there is just a small thing you haven't realised. What is (k+2)(k+1)! ? Think about it.
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    (Original post by Star-girl)
    You haven't done anything wrong - there is just a small thing you haven't realised. What is (k+2)(k+1)! ? Think about it.
    (Original post by Andy98)
    (k+1)!=?

    Yeah thanks it's just (k+2)(k+1)...3(2)(1), I think
 
 
 
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