The Harmonic Series Diverges In Example 8 we proved that the harmonic series diverges. Here we outline additional methods of proving this fact. In each case, assume that the series converges with sum S, and show that this assumption leads to a contradiction.

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= 1 + 2 n=1 n el+(1/2)+(1/3)+-.+(1/n) = e' . e/2. el/3.... e el/n %3| + 1 + 1 + 1 + = n + 1