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Find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).

  1. Dec 9, 2011 #1
    find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

    Cr represent nCr
    find the value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......(C0+C1+C2+C3+.....Cn)

    How i did it
    C0+C1+C2+.........Cn=(1+1)n
    so
    C0=(1+1)0
    C0+C1=(1+1)1 ( here n is 1)
    C0+C1+C2=(1+1)2 (here n is 2)
    .
    .
    .

    so the required question is changed into following
    20+21+22+23+..........+2n
    that's Geometric progression
    so it should equal to 2n-1

    where i have done it wrong
     
  2. jcsd
  3. Dec 9, 2011 #2

    eumyang

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    Homework Helper

    Re: find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

    Your notation is ambiguous. If Cr = nCr, then I would think that
    C0 = nC0 = 1,
    C0 + C1 = nC0 + nC1 = 1 + n,
    C0 + C1 + C2 = nC0 + nC1 + nC2 = 1 + n + n(n+1)/2.

    It looks like when you were finding
    C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......(C0+C1+C2+C3+.....Cn)
    you were actually finding
    0C0 + (1C0 + 1C0) + (2C0 + 2C0 + 2C0) + ... + (nC0 + nC0 + nC0 + ... + nC0).

    So which one are you looking for, exactly?
     
  4. Dec 9, 2011 #3
    Re: find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

    my question was correct.
    You did not answer the question but you answer you have solved my problem. that is always nCr. I take different values of n. that's what i was doing wrong.
    Thanks Bcz you put out difference in my answer and question.
    :smile:Thanks friend.:smile:
     
  5. Dec 9, 2011 #4

    Ray Vickson

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    Re: find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

    Assuming you mean C(k) = nCk for k = 0, 1, 2, ..., n, your sum, S, can be expressed as
    [tex] \begin{array}{l}S = (n+1)C(0) + n C(1) + (n-1) C(2) + \cdots + C(n) \\
    \mbox{ } = (n+1)[C(0) + C(1) + \cdots + C(n)] - [C(1) + 2C(2) + \cdots + nC(n)],
    \end{array}[/tex]
    and this last sum can be computed (do you see how?)

    RGV
     
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