Estimating infinite series Estimate the value of the following convergent series with an absolute error less than 10−3.
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- 11. Practice similar Help me with this By recognizing the series sum = −((3/4)) – as a Taylor series evaluated at a particular value of x, find the sum of the convergent series. ((3/4))² ((3/4))³ 2 ▶ ((3/4))" narrow_forwardIn the image below.arrow_forwardV12(–1)" 3" (2n + 1) V12(-1)" 3" (2n + 1) 1. Consider the series Note: this was changed from n=0 n=1 (a) Use any test for convergence/divergence to show that the series converges. V12(-1)" 3" (2n + 1) (b) It is possible to show that the sum of the series > is T, in other words, the series n=0 converges to the number T. (You do NOT need to prove this, but it can be done somewhat easily using a Taylor series expansion of arctan x.) Suppose you want to use a partial sum of this series to estimate the value of T to an accuracy of within 0.0001. Would using the first 8 terms of the series be enough to ensure you get an accuracy of within 0.0001? (8 terms means the terms where n = 0, 1, 2, 3, ...., 7.)arrow_forward
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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_forward3n Determine whether is convergent. Specifically, use the Comparison Test to compare this 22n+9.Vn n=1 series to a geometric series. 3n Claim: is convergent (please answer true or false). | 22n+9./ñ n=1 The common ratio of the geometric series suitable for applying the Comparison Test is r = 3n Claim: b, and an = r" satisfy 22n+9.Vn (1) 0 lor (2) 0 1) (please enter (1) or (2)). n2 + 5 Determine whether the series is convergent using the Comparison Test to compare it to a p- n² In n n=2 series. Hint: Recall that 0 2. n2 + 5 Claim: is convergent (please answer true or false). | n2 Inn n=2 The parameter of the p-series suitable for applying the Comparison Test is p n² + 5 1 Claim: bn and an = satisfy nP n2 Inn (1) 0 2 or (2) 0 2 (please enter (1) or (2)). IM:arrow_forwardQ// Consider the two series such that: f(x) = 1 + 2x + 3x2 +4x3 + ... and g(x) = 1 + 2x + 3x2 +4x3 + a. Find the sum of the two generating functions. Then find the generating function for the result. b. Find the product of the two generating functions. Attach File Browse My Computerarrow_forward
- ∞0 11. Discuss the convergence of the series 1/n², p > 0.arrow_forwardConsider the alternating series (-1)" t |R241 S n=1 It can be shown that this series converges by the Alternating Series Test. What is the largest possible error (remainder) in estimating the sum of the series by adding the first 24 terms? (Enter an exact value.)arrow_forward9n converges 14. Use a limit comparison to determine whether the series Ln=02+1 or diverges Compare to: which Converges / Diverges Conclusion: The series Converges / Divergesarrow_forward
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