Suppose converges. Then converges <===> converges.

Should I prove this by contradiction using partial sums of the three series? (Headbang)

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- April 27th 2010, 03:22 PMFailureEqualsLearnSum of Two Series Proof
Suppose converges. Then converges <===> converges.

Should I prove this by contradiction using partial sums of the three series? (Headbang) - April 27th 2010, 03:42 PMTikoloshe
What’s confusing is that there is only one case to show here (even though it looks as if not). Without loss of generality, assume one of them converges. Just look at the partial sums to get the final one.

Let , . Suppose and . A fundamental limit property tells us that . Thus converges. - April 27th 2010, 03:47 PMDrexel28