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find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tanx-sinx)/(sin x)cube{denominator is sine cube} as x-->0 and whose common ratio is the limit of the functin g(x)=(1-square root x)/square of cos inverse xas x approaches to 1
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Sum of an Infinite Geometric Series
The sum of an infinite geometric series is given by the formula:
\[ S = \frac{a}{1 - r} \]
where:
- \( a \) is the first term of the series
- \( r \) is the common ratio of the series

Given Functions
Let's define the functions:
- \( f(x) = \frac{\tan x - \sin x}{\sin^3 x} \)
- \( g(x) = \frac{1 - \sqrt{x}}{(\cos^{-1} x)^2} \)

Finding the Limits
As \( x \) approaches 0, the limit of \( f(x) \) is the first term of the geometric series, and the limit of \( g(x) \) is the common ratio of the series.

Calculating the Limits
1. Calculate the limit of \( f(x) \) as \( x \) approaches 0 to find the first term.
2. Calculate the limit of \( g(x) \) as \( x \) approaches 1 to find the common ratio.

Sum of the Geometric Series
Substitute the values of the first term and common ratio into the formula for the sum of an infinite geometric series to find the sum.
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find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tanx-sinx)/(sin x)cube{denominator is sine cube} as x-->0 and whose common ratio is the limit of the functin g(x)=(1-square root x)/square of cos inverse xas x approaches to 1
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find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tanx-sinx)/(sin x)cube{denominator is sine cube} as x-->0 and whose common ratio is the limit of the functin g(x)=(1-square root x)/square of cos inverse xas x approaches to 1 for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tanx-sinx)/(sin x)cube{denominator is sine cube} as x-->0 and whose common ratio is the limit of the functin g(x)=(1-square root x)/square of cos inverse xas x approaches to 1 covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tanx-sinx)/(sin x)cube{denominator is sine cube} as x-->0 and whose common ratio is the limit of the functin g(x)=(1-square root x)/square of cos inverse xas x approaches to 1.
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