Calculus II – Workshop #25 | San Diego State University

University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

417

Pages:

1
Author:

kaleidoscope71ex

Workshop #25 1. Consider the series ∞ X 2n xn n=1 5n+1 . (a) Rewrite this series (in summation notation) so that it is clear that this is a geometric series. (b) What is the common ratio? (c) Use the information you found above to determine for which values of x this series will converge. 2. Consider the series ∞ X nxn √ . n+1 n=1 an+1 . n→∞ an (b) From the information you found above, for what values of x do you know the series will converge? (a) Compute lim (c) For what values of x were you not able to determine convergence or divergence? Check those values. 3. The set of values of x for which a series converges is called the interval of convergence. Find the interval of convergence for each of the following series. (a) (b) (c) (d) ∞ X 3n xn n=1 ∞ X n=1 ∞ X n=1 ∞ X n=1 n2 √ n(x − 3)n 4n xn nn xn (n − 1)! en