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What is the value of 1+cos^1x+cos^2x+cos^3x+cos^4x+..........to infinity?
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The sum of an infinite geometric progression with the common ratio r, |r| < 1 is
S = .
Substitute here x = cos(x), and you obtain the sum of your infinite sequence
T = .
Answer. The sum = . Valid for |cos(x)| =/=1.
