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Math Help - hw problem

  1. #1
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    hw problem

    someone please help me with this. show that the convergence of a series is not affected by changing a finite number of its terms.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by gixxer998 View Post
    someone please help me with this. show that the convergence of a series is not affected by changing a finite number of its terms.
    Since there are only finitely many terms being changed, let N=\max\{i:a_i~changed\}

    Rewrite the sum as \sum_{i=1}^N a_i+\sum_{i=N+1}^{\infty}a_i.

    The left sum is just adding a finite list of numbers, so it is just a number, and the convergence of the right sum is implied by the convergence of the original sum \sum_i a_i. Thus the whole sum converges.
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  3. #3
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    Thank you so much for your help!
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