That 1 - 1 / 2 + 1 / 3 - 1 / 4 + ... -
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= 1 + 1 / 2 + 1 / 3 + ... + 1 / 2( - (1 + 1 / 2 + 1 / 3 + ... + 1 / n)
= 1 / n + 1 + 1 / n + 2 + ... + 1 / 2n
Recognize the latter expression as a Riemann sum and use it to find the sum of the alternating harmonic series?
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