Question 1062254
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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 {{{1 + r + r^2 + r^3 + ellipsis}}} with the common ratio r, |r| < 1 is

S = {{{r/(1-r)}}}.

Substitute here x = cos(x), and you obtain the sum of your infinite sequence

T = {{{cos(x)/(1-cos(x))}}}.


<U>Answer</U>. The sum = {{{cos(x)/(1-cos(x))}}}. Valid for |cos(x)| =/=1.
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