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Compute

\[1 \cdot \frac {1}{2} + 2 \cdot \frac {1}{4} + 3 \cdot \frac {1}{8} + \dots + n \cdot \frac {1}{2^n} + \dotsb.\]

 Apr 22, 2018
 #1
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Sorry, cannot read your "LaTex"!!.

 Apr 22, 2018
 #2
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Latex: \(1 \cdot \frac {1}{2} + 2 \cdot \frac {1}{4} + 3 \cdot \frac {1}{8} + \dots + n \cdot \frac {1}{2^n} + \dotsb.\)

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 Apr 22, 2018
 #3
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You can sum it up on the calculator here and it converges to 2.

 Apr 22, 2018
edited by Guest  Apr 22, 2018

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