Determine-the-convergence-intervval-of-n-0-1-n-x-1-n-

Question Number 120810 by fajri last updated on 03/Nov/20

D e t e r m i n e t h e c o n v e r g e n c e i n t e r v v a l o f :

\underset{n = 0}{\sum^{\infty}} {(- 1)}^{n} {(x - 1)}^{n}

Answered by 675480065 last updated on 03/Nov/20

\lim_{n \to \infty} ∣ \frac{U_{n + 1}}{U_{n}} ∣< 1

\Rightarrow \lim_{n \to \infty} ∣ \frac{{(- 1)}^{n + 1} {(x - 1)}^{n + 1}}{{(- 1)}^{n} {(x - 1)}^{n}} ∣< 1

\Rightarrow \lim_{n \to \infty} ∣ \frac{- {(- 1)}^{n} {(x - 1)}^{n} (x - 1)}{{(- 1)}^{n} {(x - 1)}^{n}} ∣< 1

\Rightarrow ∣ x - 1 ∣< 2 \Rightarrow - 2 < x - 1 < 2

hence - 1 < x < 3

Commented by fajri last updated on 03/Nov/20

t h a n k s s i r \dots

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