n=0 Exercise 2 Examine the following series Enon with complex links absolute convergence, i.e. you check whether To|zn| converges or not: n=0 (a) «Σ(17)", n=1 n n 1 (0) Σ (1+i), «Σ»(+)". log(n) n=2 n=2 2+
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- Find the interval of convergence for the power series (-1)" Vn 5n (* – 3)". - n=1Find a power series representaton for f(x) = 1/(5+2x)Find the radius and interval of convergence for the following series: (x - 2)" 10n a. n=0 Radius= Interval= Σ n=0 Radius= b. (-1)"x" n! Interval= C. Σ(n!) (x - 4)" n=0 Radius= Interval=
- Use the power series 00 f(x) = Σ 1 1 + x n=0 to determine a power series for the function, centered at 0, 16 d² 8 (x + 1)³ dx² x + 1 = f(x) = Σ (-1)^x", Ixl < 1 n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)What are the first non-zero terms of the Taylor series, the power series written in sigma notation, and the interval of convergence for the function f(x)=log3(x+1) with a=0?Find the radius and interval of convergence for the following series: (x - 2)" 10" a. n=0 Radius= 10 Interval = b. Σ n=0 Radius= (-1)" xn n! (-8,12) C. Interval= (-∞0,00) 8 Σ(n!) (x-4)" n=0 Radius= Interval=
- Use the power series 00 E(-1)^x" 1 + x n = 0 to determine a power series, centered at 0, for the function. 1 dx х+ 1 f(x) = In(x + 1) = f(x) = > n = 0 Identify the interval of convergence. (Enter your answer using interval notation.)Find the interval of convergence of the power series ∑n=3∞ ((-1)n(n-2)/n22n)(x-2)nExercise 4.1 Find the radius and interval of convergence for the following series. 1. En-1n+1 2. En-1)"x" 3. En=1n n=1 4. En=12(x- 3)" 5. ΣΗ- 6. Σ-1 (-1)"x+1 (n+1)! 7. En=1 (-1)"(x-2)" 8. Ln-1 2 (n+1) 9. En=1 10. E-1n(x+ 5)"
- Find the radius and interval of convergence of the given power series (-1)"n²(x + 2)" U. 3n5. Suppose that the power series E Cnx" converges when x = 3 and diverges when x = 6. Which of the following n=0 statements is certain to be true? (a) None of these statements is certain to be true. (b) Σ Cn(-4)" is convergent. n=0 (c) Σ Cn(-3)" is convergent. n=0 (d) > Cn(-2)" is convergent. n=0 (e) 2 Cn(-6)" is divergent. n=0Find a power series for the function, centered at C and determine the interval of convergence (function is h(x) and C = 0).h(x)=1/(1-5x) Also see the attached picture of the problem.