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Those infinite small steps (Posted on 2006-10-03) Difficulty: 2 of 5
Show that 1+1/2+1/3+1/4+...is infinite.

No Solution Yet Submitted by Art M    
Rating: 3.6667 (3 votes)

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Solution Another one | Comment 5 of 8 |
Assume the sum is finite and let's call it S. Then

S=1+1/2+1/3+1/4+1/5+1/6... > 1/2+1/2+1/4+1/4+1/6+1/6...
= 2*(1/2+1/4+1/6...) = 2*S/2 = S

Follows S>S. Contradiction, therefore S is not finite.

  Posted by JLo on 2006-10-03 15:33:22
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