(2) Alternating Harmonic Series Revisited What is wrong

(2) Alternating Harmonic Series Revisited What is wrong here: Multiply both sides of the alternating harmonic series S = 1- ½ +1/3 ? ¼ +1/5 -1/6 +1/7 -1/8 +1/9 -1/10 +1/11 -1/12 +? By 2 to get 2S = 2 -1+2/3 -1/2+2/5-1/3+2/7-1/4+2/9-1/5+2/11-1/6+? Collect terms with the same denominator (match the colors, etc …) to get 2S =1-1/2 +1/3 -1/4 +1/5 -1/6 +?= S. Dividing by S gives 2 = 1.

Solution

Here \”S\” is equals to zero, so we cannot divide out \”S\” from both sides from the equation \”2S=S\”. So if we simplify it we get,

2S=S

2S-S=0

S=0

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