Paper Folding Constant

Author

Eric W. Weisstein
August 9, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/PaperFoldingConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PaperFoldingConstant.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Sum

Analytic

Sum[(1/(2^(2^k)))(((1-(1/(2^(2^(k+2))))))^(-1)),{k,0,∞}]

FullSimplify[(1/(2^(2^k)))(((1-(1/(2^(2^(k+2))))))^(-1)),k∈Integers&&k>0]

Sum[((8^(2^k))/(-1+(2^(2^(2+k))))),{k,0,∞}]

Numerical

N[Sum[(1/(2^(2^k)))(((1-(1/(2^(2^(k+2))))))^(-1)),{k,0,20}],1000]

N[Sum[(1/(2^(2^k)))(((1-(1/(2^(2^(k+2))))))^(-1)),{k,0,21}],1000]

NSum[(1/(2^(2^k)))(((1-(1/(2^(2^(k+2))))))^(-1)),{k,0,∞},WorkingPrecision->1000]