Problem 3

Due in DSC 203 by 3 PM, Friday, September 14, 2001

Suppose that $0<x<\pi/2$ and let

$$\begin{eqnarray*}S_1&=&1+\cos^2x+\cos^4x+\cdots \\ S_2&=&1+\sin^2x+\sin^4x+\cdots \\ S_3&=&1+\cos^2x\sin^2x+\cos^4x\sin^4x+\cdots \end{eqnarray*}$$

Show

$$S_1+S_2=S_1S_2\qquad\mbox{and}\qquad S_1+S_2+S_3=S_1S_2S_3.$$

Solutions, questions and/or comments should be directed to Judy Downey or Griff Elder

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Last modified:   Thu Sep 6 16:27:23 CDT 2001