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Gabriel's Staircase

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GabrielsStaircase

The series

sum_(k=1)^inftykr^k=sum_(k=1)^inftysum_(i=k)^inftyr^i=r/((1-r)^2),

valid for 0<r<1.

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References

Swain, S. G. "Proof without Words: Gabriel's Staircase." Math. Mag. 67, 209, 1994.

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Gabriel's Staircase

Cite this as:

Weisstein, Eric W. "Gabriel's Staircase." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GabrielsStaircase.html

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