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Otrada [13]
3 years ago
8

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv

al. If the answer is arn interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)
[infinity]

Σ (-1)n+1(x-8)/n8n

n=1
Mathematics
1 answer:
Anon25 [30]3 years ago
3 0

I'm guessing the power series given is

\displaystyle \sum_{n=1}^\infty (-1)^{n+1}\frac{(x-8)^n}{8^n}

which you can condense somewhat into

\displaystyle -\sum_{n=1}^\infty \left(\frac{8-x}8\right)^n

You should recognize this as a geometric series, which converges for

\left|\dfrac{8-x}8\right|

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