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Is this a geometric progression? or binomial expansion i'm not sure how they got 10^9

  1. Nov 12, 2006 #1
    Hello everyone.

    I'm studying for my exam and i'm reveiwing some problems but this one isn't making sense to me:

    11^9(9 choose 0) - 11^8(9 choose 1) + 11^7(9 choose 2) - .... - 11^2(9 choose 7) + 11^1 (9 choose 8) - 11^0 (9 choose 9)


    answer:
    (11-1)^9 = 10^9 = 1,000,000,000.

    work looked like:
    (9 choose 0) 11^9 (-1)^0 + (9 choose 1)11^8(-1)^1


    Can someone explain to me how they did this?
    I see the 11 is decreasing, and the signs are alternating, it looks like a binomial expansion but i'm not seeing how they simplified that.

    Thanks
     
  2. jcsd
  3. Nov 13, 2006 #2

    Office_Shredder

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    It IS a binomial expansion. It's 11k*(-1)9-k*9choosek with k going from 0 to 9

    Try expanding (11-1)9 and compare them
     
  4. Nov 13, 2006 #3
    [​IMG]

    So would
    a = 11
    and
    b = -1
    and
    n = 9

    (11-1)^9 = (9 choose 0)11^9 + (9 choose 1)11^8*(-1) +(9 choose 2)11^7*(-1)^2......

    I see this is going to work, from the written out expansion, i can see n = 9, b = -1, a = 11,


    ahh i got it@!

    thank u!
     
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