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Math Help - Monotone Sequences

  1. #1
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    Monotone Sequences

    Suppose that absolute value of (c) is less than 1 and that, for every positive integer n,
    (X sub n) = the summation from i=1 to n, of c^(i-1)

    Explain why,
    (X sub n) approaches (1/(1-c))

    Thanks for your help!!
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  2. #2
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    Quote Originally Posted by Slazenger3 View Post
    Suppose that absolute value of (c) is less than 1 and that, for every positive integer n,
    (X sub n) = the summation from i=1 to n, of c^(i-1)

    Explain why,
    (X sub n) approaches (1/(1-c))

    Thanks for your help!!

    It's the sum of a geometric series: \sum^n_{i=0}r^i=\frac{1-r^{n+1}}{1-r} , so now you've to take the limit in both sides when n\rightarrow \infty , and....what's the limit of r^n\,,\,\,|r|<1 ? Exactly!

    Tonio
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