(d) Let (c) be a convergent sequence such that lim n = L where L 0. Cn+1 i. Show that lim = 1. 2004-2 11-∞ ii. Hence or otherwise, determine the radius R of convergence for the series ∞ Σcka. Analyse the convergence of the series for x = ±R. k=1

Entered DIV 0.25 At least one of the answers above is NOT correct. (a) The series Σ(An). Div n=1 Answer Preview (b) The sequence {An}. DIV Given: 3n An = 12n + 13 For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, -INF if it diverges to minus infinity, or DIV otherwise. 1 4

Determine the series of the given function. Write out the sum of the first four nonzero terms of the series representing this function. Determine the interval of convergence a) g(x) = In( 1 - 2 x ) %3D b) f(x)= 7/(5+x^2)

(2+x)" Q4. Find the convergence interval and radius of the series : E (-1)**" 2" n n=1

npt=19963228&cmid%3892678&page%3D2 Spring21 Question 5 2k-1 Determine if the series converges or diverges. If convergent, find the sum of the series Not yet answered Select one: Marked out of O a. Converges to 1.6 P Flag question O b. Diverges O c. Converges to - O d. None of these Question 6 (x+ 즐)" The third non-zero term in the Taylor series of f(ar) = sin z centered at Not yet is 2 4! answered Marked out of Select one: 1.6 O a. True P Flag question Ob. None of these False EGO 121

(-1)^ + 1 The series 2 is a convergent series. n = 1 (n³)(2") a. Approximate the sum of this series using its first 4 terms. b. What is the error in this approximation? c. Give the smallest interval in which the exact sum must lie.

Expand the function s in a power series E a,x" with center e = 0. Find anx". n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form (-1)" in your answer.) anx" Determine the interval of convergence. (Give your answers as intervals in the form (*, *). Use symbol co for infinity, U for combining intervals, and appropriate type of parenthesis " (", ")","[" or "] " depending on whether the interval is open or closed. Enter DNE if interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) x E

Consider the power series (-1)"(-2x + 5)" 5" (n² + 9) Find the center and radius of convergence R. If it is infinite, type "infinity" or "inf". Center a = Radius R = n=1 What is the interval of convergence? ⠀ Give your answer in interval notation.

Please explain why sequence Xnk approaches +infinity and why sequence Xmk approaches -infinity. Why would one use each of the sequences if the main sequence is (n sin n)? Lastly, can I assume sequence sequence Nk sin Nk <1/2 ...therefore making it convergent? Why the other way?

Determine the radius of convergence and the interval of convergence for the power series: