If ∣ x ∣ < 1 and y = x − 2 x 2 + 3 x 3 − 4 x 4 + ……… . . then x =

y = x − x 2 + 3 x 3 − 4 x 4 + … . y = lo g e ( 1 + x ) ⇒ 1 + x = e y ⇒ x = y + 2 ! y 2 + 3 ! y 3 + …

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremLogarithmic and Exponential seriesMedium2 minQB

MathematicsMediumsingle choice

If $∣ x ∣ < 1$ and $y = x - \frac{x ^{2}}{2} + \frac{x ^{3}}{3} - \frac{x ^{4}}{4} + \dots\dots\dots .$ . then $x =$

Answer:

Solution:

$y = x - x^{2} + \frac{x ^{3}}{3} - \frac{x ^{4}}{4} + \dots$ .

$y = lo g_{e} (1 + x) \Rightarrow 1 + x = e^{y}$

$\Rightarrow x = y + \frac{y ^{2}}{2 !} + \frac{y ^{3}}{3 !} + \dots$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Logarithmic and Exponential series

⏱ 2mℹ️ Source: QB

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