If a power series $\sum a_{k} x^{k}$ converges at x = 6 and x = 7 then it converges at x = -6.

Name: If a power series $\sum a_{k} x^{k}$ converges at x = 6 and x = 7 then it converges at x = -6.
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Question

Quizplus · Accepted Answer

The convergence of a power series at a point $x = a$ implies convergence for all $x$ such that $|x| < |a|$. Since the series converges at $x = 6$ and $x = 7$, it must also converge for all $x$ within the radius of convergence, which includes $x = -6$, as $|-6| = 6 < 7$.

If a Power Series ∑akxk\sum a_{k} x^{k}∑ak​xk Converges at X = 6 and X = 7 Then

If a Power Series $\sum a_{k} x^{k}$ Converges at X = 6 and X = 7 Then