high light only Ex. 3.2. Determine the values of x E R for which the following...
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Ex. 3.2. Determine the values of x € R for which the following series con- verge pointwise. 2η (1) Σ2nα (ii) 2η 1+ 2η (2+1)2η n=0 n=0. Με Με Με n=0 | 3η (8) Σ" hete") (vi) Σ. (vii) Σ α ” ln(") n=1 (1) Σεπ 1η-2η 1+0202 = 1
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Ex. 3.1. Determine, when possible, the function f(x) to which the following sequences converge in a pointwise way: sin(na) (ii) (i) n 2n (iii) 1 2n (iv) n (v) n! (vi) x
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Ex. 2.12. Miscellaneous. Determine whether the following series are con- vergent or divergent. Zn2 En m3 m3"(7) n2 +n (1+n2 n=1 n = © SUT, May 23, 2019 64 Module 2. Numerical Series N= 0 Vn2 +1-n (3n)! nn!)3 n2 + Inn vn n=1 ( 8 (-:-)" so Živa – vn = 1)
1. Find the first four power series terms of f(x) e sinx and compare values of f(.2) with the value from the 2n+1 ex: Σ(-1)" and sinx2(-)" n! series. {3 decimal places) Multiple the series
1. Find the first four power series terms of f(x) e sinx and compare values of f(.2) with the value from the 2n+1 ex: Σ(-1)" and sinx2(-)" n! series. {3 decimal places) Multiple the series
2. Determine the values of x for which the given series converges absolutely, converges conditionally or diverges. Σ (x+3)" 2n +3 n=1
(1) Determine whether the following series converge or diverge: (a) Σ=0 η2 n=1 (b) Σ=0 520 και (c) Σ=2 /n ln (η) 2n (4) Σ. sin(1) η2 (e) Σ1 (1) Σ=1 n2-3n+1 ln(η).
Determine the Taylor Series for the function f(x) = e-3 centered at α = -1. ΑΣ-3)* * (t+ 1): Β. Σ" (a + 1): «Σ " (a + 1)" b. Σ-30" d';" Σε «-): Ε Σ - 1): Using the Maclaurin Series for et, which of the following series sums to the ΑΣ ΣΕ «ΣΗ Σ 8
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ple 2. Find 3. Determine which of the following series converge. Justify your conclusions with the appro -1)" In n (c) Σ dots not 4. Suppose we know that 0 S on S 1/n S an and that 0sn S1/n2 sd for all n. (a) Which of the series Σα", Σ h,De-, and Σ d" definitely converge? Justify your answer. (b) Which of the series Σα", Σ " Σ c", and Σ d"...
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Determine whether the series n-1 Σ (2n)! 2". (2n! converge or diverge 1. both series converge 2. only series II converges 3. only series I converg es 4. both series diverge Determine whether the series 2! 1515.9 1-5.9-13 3! 4! 7m 1.5.9..(4n -3) is absolutely convergent, conditionally con- vergent, or divergent 1. conditionally convergent 2. absolutely convergent 3. divergent Determine which, if any, of the...
(b) Determine for which values of x the following series converges and find the limit for all the values of x where the series converges: (-1)" sin(ne) n n=1 Does this series converge uniformly on R? (c) Find the value of M8 1 n4 n=1