Mathematics: Solve for the nearest whole number

and the interval of the convergence is (-1, 1)Step-by-step explanation:To find a power series for the function, centered at c.If we factorize the denominator, we have:Thus;and the interval of the convergence is (-1, 1)...

Solve for the nearest whole number - id12231666, Tyrant4life

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frenchpotaetoes2832

24.08.2020

Mathematics

$\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }$

and the interval of the convergence is (-1, 1)

Step-by-step explanation:

To find a power series for the function, centered at c.

$g(x) = \dfrac{7x}{x^2 +5x-6} ,\ c = 0$

If we factorize the denominator, we have:

$g(x) = \dfrac{7x}{(x +6)(x-1)}$

$g(x)= \dfrac{1}{x-1}+\dfrac{6}{x+6}$

Thus;

$g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1+\dfrac{x}{6}}$

$g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1-(-\dfrac{x}{6})}$

$g(x) = - \sum \limits^{\infty}_{n=0} x^n + \sum \limits^{\infty}_{n=0} x^n(\dfrac{-x}{6})^n \ \ if \ \ |x| < 1 \ \ and \ \ |\dfrac{x}{6}< 1$

$g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n , \ if |x|$

$\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }$

and the interval of the convergence is (-1, 1)

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Solve for the nearest whole number

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