If -x-1 and y-1-x-x2-x3- then write the value of d y d x-

The given series is a geometric series where a = 1 and r = x. fx=1+x+x2+x3+...=11 xSum #160;of #160;the #160;infinite #160;series #160;of #160;a # ...

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Standard XI

Mathematics

Differentiability

If |x|<1 and ...

Question

If |x| < 1 and y = 1 + x + x² + x³ + ..., then write the value of $\frac{d y}{d x}$ .

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Solution

The given series is a geometric series where a = 1 and r = x.
$f (x) = 1 + x + x^{2} + x^{3} + . . . = \frac{1}{1 - x} (Sum of the infinite series of a geometric series is \frac{a}{1 - r} .) f' (x) = \frac{- 1}{(1 - x)^{2}} \frac{d}{d x} (1 - x) = \frac{- 1}{(1 - x)^{2}} (- 1) = \frac{1}{(1 - x)^{2}}$

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