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Originally Posted by 1010011010
Why is it that the sum of 4/{n[(-1)^(1+n)]} approaches pi (of the 3.14159... variety)?
This is the 4/1-4/2+4/3-4/4+4/5-4/6+4/7... series. It doesn't seem like there's any reason that it should.
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Conditionally convergent series can be made to add up to different numbers depending on the sequence and the order of its terms. That there is one that adds up to pi shouldn't surprise you anymore than one that sums to two.