Teacher2Teacher 
Q&A #267 
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From: Mr. Leohr <jnmleohr@adelphia.net> To: Teacher2Teacher Public Discussion Date: 2003111823:50:18 Subject: Another fun proof that shows 2 = 1 Here's another proof that shows 2 = 1 that requires some knowledge of infinite series. If S = 1  1/2 + 1/3  1/4 + 1/5 ... and 2S = 2  1 + 2/3  1/2 + 2/5  1/3 + 2/7  1/4 ... which can be simplified by grouping terms to 2S = (21)  (1/2) + (2/3  1/3)  1/4 ... 2S = 1  1/2 + 1/3  1/4 + 1/5 ... So 2S = S and if we divide both sides by S then 2 = 1 Here's where we went wrong... In infinite series, you are not allowed to reorder the elements. It is not commutative under addition. Crazy huh? Mr. Leohr
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