If y = x - frac{x^2}{2} + frac{x^3}{3} - dots | vedclass

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(B) The given series is the expansion of the logarithmic function: $y = x - \frac{x^2}{2} + \frac{x^3}{3} - \dots = \ln(1 + x)$ Taking the exponential

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$y + \frac{y^2}{2!} + \frac{y^3}{3!} + \dots \infty$

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(B) The given series is the expansion of the logarithmic function: $y = x - \frac{x^2}{2} + \frac{x^3}{3} - \dots = \ln(1 + x)$ Taking the exponential of both sides: $e^y = 1 + x$ Rearranging for $x$: $x = e^y - 1$ Using the exponential series expansion $e^y = 1 + \frac{y}{1!} + \frac{y^2}{2!} + \frac{y^3}{3!} + \dots$: $x = (1 + \frac{y}{1!} + \frac{y^2}{2!} + \frac{y^3}{3!} + \dots) - 1$ $x = y + \frac{y^2}{2!} + \frac{y^3}{3!} + \dots$

If $y = x - \frac{x^2}{2} + \frac{x^3}{3} - \dots \infty$,then $x = $

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