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Math Help - Does the subtraction of 2 diverging Series mean the resulting Series is convergent?

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    Does the subtraction of 2 diverging Series mean the resulting Series is convergent?

    An=Bn-Cn Bn and Cn are both diverging Does An converge??
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  2. #2
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    Quote Originally Posted by Some1Godlier View Post
    An=Bn-Cn Bn and Cn are both diverging Does An converge??
    Definitely not!

    Consider B_n=n^2 \text{ and} C_n=5n^4

    Clearly the difference diverges as well. The difference can sometimes lead to a converging series but you need to use convergence tests to verify. An example of such a case is a telescoping series, where almost all the terms cancel out and the remaining terms sum to a finite value.
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  3. #3
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    well let a_n=b_n=n, both divergent series, but the difference converges.

    of course, just a particular case.
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