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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 One proof out of many | Comment 1 of 8
Wonder how many other solutions we can get for this classic. Here is mine:

S_n:=1/(2^n+1)+1/(2^n+2)+1/(2^n+3)+...+1/(2^(n+1))>=2^n*1/(2^(n+1))=1/2
therefore
1+1/2+1/3+1/4+... = 1+S_0+S_1+S_2+...>= 1+1/2+1/2+1/2+...


Edited on October 3, 2006, 8:22 am
  Posted by JLo on 2006-10-03 06:30:45

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