Riemann Series Theorem

The Riemann series theorem states that by a suitable rearrangement of terms, a conditionally convergent series may be made to converge to any desired value, or to diverge.

For example,

			(1)
			(2)
			(3)

converges to , but the same series can be rearranged to

			(4)
			(5)
			(6)
			(7)

so the series now converges to half of itself.