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Binomial series problem

  1. Oct 12, 2010 #1
    I havn't done this in a long time! And apparently I should know this easy, it sort of looks like a proof by induction, which I havn't done before and I am frantically trying to learn!

    Show that for each integer n the alternating sum of binomial coefficients:

    1 - (n) + ... + (-1)^k(n) + ... + (-1)^(n-1)( n ) + (-1)^n
    .....(1)....................(k)................... .......(n-1)
    is zero. What is the value of the sum

    (so what ive done here is started with an "inductive basis of n=1 which kind of suggests it goes to zero but without the appropriate conciseness)

    1 + (n) + ... + (n) + ... + ( n ) +1
    ......(1)...........(k)...........(n-1)

    I understand the layout is a bit rubbish but I hope you can fathom it!
    Any help would be greatly appreciated!

    UPDATE! After a bit of research, am I correct in assuming this is a telescoping series?
     
  2. jcsd
  3. Oct 12, 2010 #2
    "Binomial" is the key word here. Try to find a clever way to manufacture what you see in front of you by expanding some expression.
     
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