If the infinite sum \(\dfrac1{2^1}+\dfrac1{2^2}+\dfrac1{2^3}+\dfrac1{2^4}+\cdots =1,\) what is the value of the infinite

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If the infinite sum \(\dfrac1{2^1}+\dfrac1{2^2}+\dfrac1{2^3}+\dfrac1{2^4}+\cdots =1,\) what is the value of the infinite sum \(\dfrac1{2^1}+\dfrac2{2^2}+\dfrac3{2^3}+\dfrac4{2^4}+\cdots ?\)

A. \(1\)
B. \(2\)
C. \(3\)
D. \(\pi\)
E. Infinite

Answer: B

Source: Veritas Prep
Source: — Problem Solving |