Cookson Hills Series

Author

Eric W. Weisstein
April 29, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/CooksonHillsSeries.nb.

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

©2011 Wolfram Research, Inc. except for portions noted otherwise

(∑_(n=1)^∞)(1/((n^3) (cos^2)(n)))

Sum

V5

Sum[(1/((n^3)((Cos[n])^2))),{n,∞}]

V7

Sum[(1/((n^3)((Cos[n])^2))),{n,∞}]//Timing

SumConvergence[(1/((n^3)((Cos[n])^2))),n]//Timing

...wrong (unknown)...

V8

Sum[(1/((n^3)((Cos[n])^2))),{n,∞}]//Timing

SumConvergence[(1/((n^3)((Cos[n])^2))),n]//Timing

Table

N[Table[Sec[n],{n,100}],10]

HighWaterMarks[Abs[Table[Sec[n],{n,10^4}]]]//Timing

N[%[[2,1]]]

Graphics

g1=ListPlot[FoldList[Plus,0,N[Table[(1/((n^3)((Cos[n])^2))),{n,10^4}],100]],PlotJoined->True,PlotStyle->Red,PlotRange->All,AxesLabel->TraditionalForm/@{n,(Subscript[S, 2])[n]}]

g2=ListPlot[FoldList[Plus,0,N[Table[(1/((n^3)((Cos[n])^2))),{n,10^4}],100]],PlotJoined->True,PlotStyle->Red,AxesLabel->TraditionalForm/@{n,(Subscript[S, 2])[n]}]

Show[GraphicsArray[{g1,g2}],ImageSize->500]