Find-the-value-of-x-for-which-n-0-n-16-3-4-x-1-n-a-Is-convergent-b-Is-equal-to-10-2-3-

Question Number 92324 by I want to learn more last updated on 06/May/20

Find the value of x for which \underset{n = 0}{\sum^{n = \infty}} 16 {(\frac{3}{4} x + 1)}^{n}

(a) Is convergent

(b) Is equal to 10 \frac{2}{3}

Answered by mr W last updated on 06/May/20

c o n v e r g e n t i f

∣ \frac{3}{4} x + 1 ∣< 1

- 1 < \frac{3}{4} x + 1 < 1

\Rightarrow - \frac{8}{3} < x < 0

S = 16 \times \frac{1}{1 - (\frac{3}{4} x + 1)} = \frac{32}{3}

\Rightarrow x = - 2

Commented by I want to learn more last updated on 06/May/20

Thanks sir