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Alternate between picking the positive terms of the series for a while, then picking
the negative terms. This produces a sequence of partial sums which alternately increase
then decrease. Arrange that this oscillation takes place on either side of the number
`a`, as shown:

Moreover (as in the picture) make sure that the sequence of partial sums
reverses its direction each time it crosses from one side of `a` to the other.
Thus the partial sums are always within one term of the original series of `a`.
Since the terms of the series converge to zero (the series is convergent) the partial
sums of the rearranged series must converge to `a`.