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If |X| < 1 and Y = 1 + X + X2 + X3 + ..., Then Write the Value of D Y D X - Mathematics

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If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\] 

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Solution

The given series is a geometric series where a = 1 and r = x. 

\[f\left( x \right) = 1 + x + x^2 + x^3 + . . . = \frac{1}{1 - x}\]
\[\left( \text{ Sum of the infinite series of a geometric series is }\frac{a}{1 - r}. \right)\]
\[f'\left( x \right) = \frac{- 1}{(1 - x )^2}\frac{d}{dx}(1 - x)\]
\[ = \frac{- 1}{(1 - x )^2}( - 1)\]
\[ = \frac{1}{(1 - x )^2}\] 

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 13 | Page 47

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