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Tuesday, April 27, 2010

Problems 003

What is 1/1 + 2/2 + 3/4 + 4/8 + 5/16 + 6/32 + ...?

2 comments:

  1. We can write this:
    1/1 + 1/2+1/2 + 1/4+1/4+1/4 + 1/8+1/8+1/8+1/8 + ...
    It is absolutely convergent, so we can rearrange it:
    (1/1+1/2+1/4+...)+(1/2+1/4+1/8+...)+(1/4+1/8+1/16...)+....
    =2+1+1/2+1/4+1/8+...
    =4

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  2. Yup. I included 003 for the sake of 004.

    ReplyDelete