Combining power series Use the power series representation
to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.
39. p(x) = 2x6 ln (1 − x)
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- write expansion of function as a power seriesarrow_forwardFind the radius of convergence of the power series. (-1)"x" En=0| SMarrow_forwardsum Sn. (b) Use (a) to determine whether the series is convergent or divergent. 8 (5) Decide whether each of the following statements is true or false. If a statement is true, explain why. If a statement is false, provide specific examples of ak and Σb for k=1 which the statement is false. Σ (a) If 5 am is a series such that ak a k=1 1 k² < ak for all k, then (d) If ak k=1 (b) If ak is a series such that 0 < aarrow_forwardhow do i solve the attached calculus question?arrow_forwardH.W 1/ For the following series: - 1 (x-2), (x-2)2 (x-2)" 21 S(x) +(-1)". Find: - a- Values of (x) that make series converged b- The sum of series Ans/ a) 0arrow_forwardEvaluate the infinite series by identifying it as the value of an integral of a geometric series. (- 1)" 57+ (n + 1) 8. n+1 1 | f(t)dt where f(x) = (– 1)" Hint: Write it as 5 + I n=0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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