Find the interval of convergence of the given Taylor series representation.
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A) -4

Question

Find the interval of convergence of the given Taylor series representation.
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A) -4 < x < 4 
B) -3 < x < 3 
D) -1 < x < 1

Quizplus · Accepted Answer

Without the actual series representation, it is impossible to determine the exact interval of convergence. However, the interval of convergence for any Taylor series centered at some point $a$ will always be an interval around $a$. Since the possible choices are all centered at $0$, the correct choice must be an interval of the form $-r < x < r$ for some positive value $r$. Only choice A satisfies this requirement.

Find the Interval of Convergence of the Given Taylor Series