Problems 003 Get link Facebook X Pinterest Email Other Apps By Wabulon - April 27, 2010 What is 1/1 + 2/2 + 3/4 + 4/8 + 5/16 + 6/32 + ...? Get link Facebook X Pinterest Email Other Apps Comments Jared9:53 AMWe 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+...=4ReplyDeleteRepliesReplyWabulon7:18 PMYup. I included 003 for the sake of 004.ReplyDeleteRepliesReplyAdd commentLoad more... Post a Comment
We can write this:
ReplyDelete1/1 + 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
Yup. I included 003 for the sake of 004.
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