Question
For $0<\phi<\pi / 2$, if $x=\sum_{n=0}^{\infty} \cos ^{2 n} \phi, y=\sum_{n=0}^{\infty} \sin ^{2 n} \phi$, and$z=\sum_{n=0}^{x} \cos ^{2 n} \phi \sin ^{2 n} \phi$, then $x y z=$(A) $x y+z$(B) $x z+y$(C) $x+y+z$(D) $y z+x$
Step 1
These are geometric series with common ratios $\cos^2\phi$ and $\sin^2\phi$ respectively. So, we can use the formula for the sum of an infinite geometric series, which is $\frac{a}{1-r}$ where $a$ is the first term and $r$ is the common ratio. Show more…
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