It's easier to take their difference

Algebra Level 3

\[ \dfrac1{2^1} + \dfrac1{2^2} + \dfrac1{2^3} + \dfrac1{2^4} + \cdots , \quad \quad \dfrac1{2^1} + \dfrac2{2^2} + \dfrac3{2^3} + \dfrac4{2^4} + \cdots \]

I have written two series above. What is the ratio of values between the larger series and the smaller series?

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