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Math Help - Constant of a series from Integration

  1. #1
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    Constant of a series from Integration

    When integrating a series, the constant from the integration is evaluated as part of the summation or is it as a constant "outside" of the whole summation?

    Say I have

    Then is the result equals to this: ?

    Or is the result equals to this: ?

    Thanks!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Either way is correct.

    The C in your second equation equals the sum of C's in your first equation.
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  3. #3
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    But how would it be the same?

    In the first one, if say after some working, I found out that C=5. Then there is a summation of 5 for infinity times(which results in infinity) and then plus the summation of Xn.
    But in the second one, if C=5, it would just be the summation of Xn and then plus 5, wouldn't it?
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by xEnOn View Post
    But how would it be the same?

    In the first one, if say after some working, I found out that C=5. Then there is a summation of 5 for infinity times(which results in infinity) and then plus the summation of Xn.
    But in the second one, if C=5, it would just be the summation of Xn and then plus 5, wouldn't it?
    The C's in your first equation probably form a convergent sequence, whose sum is the C in your second equation.
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  5. #5
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    The sum of constants is still a constant...
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