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Series Expansion, inbuilt limit, geometr...

Series Expansion, inbuilt limit, geometrical limits

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Find the sum of an infinite geometric series whose first term is the limit of the function f( x) =( tan x - sinx )/( sin^(3) x ) as x rarr 0 and whose common ratio is the limit of the function g(x) = ( 1-sqrt(x))/( (cos^(-1)x ) as x rarr 1

Find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tan x-sin x)/(sin^(3)x) as x rarr0 and whose common ratio is the limit of the function g(x)=(1-sqrt(x))/((cos^(-1)x)^(2)) as x->1