Combining power series Use the geometric series
to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.
29.
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- n3=. Exercise 6. Find the sum below and the interval of convergence as well as the radius of convergence. (a) f(x) = E (x + a)" bn+1 n=1 (b) Using part a) find a geometric series such that the interval of convergence is (-15, 1).arrow_forwardCalculus IIarrow_forward00xk Use the power series f(x) = In (1-x) = - Σ, for -1arrow_forward∞0 11. Discuss the convergence of the series 1/n², p > 0.arrow_forwardIn the image below.arrow_forward1a. Find the power series representing the function 1/(z – 3) in the following regions: | z-4|5 Express your answers in the form below (minimum of four terms): 1 = a1 + az + az + a4 ... Z - 3arrow_forward1,: ? Credit Union National-Association- Using series, evaluate the inteġral I = [ f(x) dx, where f is the function whose graph is shown below. Hints: (i) The area of a triangle is (basex height). (ii) Compute the areas A1, A2, etc.., find a pattern and sum them A4 A3 A2 y=f(x) A1 0.. 1 72 2 X2 1. Apr/2021 5:00 Jain 5:00-6:10 PDT Mencses wided to Jonathaarrow_forwardPlease explain what kind of formula and method I should use to answer this question. Thank you!arrow_forwardarrow_back_iosarrow_forward_ios
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