Question

Question Determine the interval of convergence for the function represented by the series below. $sum_{n=0}^{infty} frac{1}{(x-4)^{7n-7}}$ Write your answer in interval notation, and join multiple intervals with U if necessary. Provide your answer below:

          Question
Determine the interval of convergence for the function represented by the series below.
$sum_{n=0}^{infty} frac{1}{(x-4)^{7n-7}}$
Write your answer in interval notation, and join multiple intervals with U if necessary.
Provide your answer below:

$Question Determine the interval of convergence for the function represented by the series below. sumn=0^infty frac1(x-4)^7n-7 Write your answer in interval notation, and join multiple intervals with U if necessary. Provide your answer below:$

Added by Carlos M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

07/25/2023

Step 1

The series is: $$\sum_{n=1}^{\infty} (n-7)x^n$$ Now, we will use the Ratio Test to determine the interval of convergence. The Ratio Test states that if: $$\lim_{n\to\infty} \left|\frac{a_{n+1}}{a_n}\right| < 1$$ then the series converges. In our case, $a_n = Show more…

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Determine the interval of convergence for the function represented by the series below. Write your answer in interval notation, and join multiple intervals with U if necessary. Provide your answer below: