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Math Help - sigma notation and telescoping

  1. #1
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    sigma notation and telescoping

    hi, i have a telescoping problem. i looked up the definition of "telescoping" and found as follows:
    when each term of a sum cancels part of the next term, leaving only portions of the first and last terms at them end the sum is said to "telescope."

    So, I have to evaluate the telescoping sum of:

    the summation of (a to the base of k) - (a to the base of k-1) from k=1 to n


    any tips would be appreciated thanks in advance!!
    Last edited by andyaddition; February 18th 2009 at 12:56 PM.
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  2. #2
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    Hello, andyaddition!

    I'd love to help you, but I don't understand your language . . .


    the summation of (a to the base of k) - (a to the base of k-1) from k=1 to n
    . . . . . . . . . . . . . \______________/
    . . . . . . . . . . . . .
    What does that mean?
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  3. #3
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    i'm sorry i wasn't sure how to type that. it is an "a" with a subscript/base of "k"
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  4. #4
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    Simply expand it:
     \sum_{k=1}^n \left(a_k - a_{k-1}\right)  = \left(a_1 - a_0\right) + \left(a_2 - a_1\right) + \left(a_3 - a_2\right) + \left(a_4 - a_3\right) + {\color{white}.} \  \cdots + \left(a_{n-3} - a_{n-4}\right) + \left(a_{n-2} - a_{n-3}\right) + \left(a_{n-1} - a_{n-2}\right) + \left(a_{n} - a_{n-1}\right)

    Now look carefully. What terms cancel out and what terms are left?
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