- #1
nns91
- 301
- 1
Homework Statement
The MacLaurin series for ln(1/1-x) is sum of x^n/n with interval of convergence -1<= x <1
a. Find the Maclaurin series for ln(1/1+3x) and determine the interval of convergence
b. Find the value of [tex]\sum[/tex] (-1)^n/n from n=1 to infinity.
c. Give a value of p such that [tex]\sum[/tex] (-1)^n/ n^p converges but [tex]\sum[/tex] of 1/n^(2p) diverges. Give reasons why your value of p is correct.
d. Give a value of p such that [tex]\sum[/tex]1/n^p diverges but [tex]\sum[/tex]1/n^(2p) converges. Give reasons why your value of p is correct.
Homework Equations
Limit test
The Attempt at a Solution
a. So I guess the answer for the series is [tex]\sum[/tex](-1)3x^n/n. Am I right ?
b. How do I do this one ?
c. I am not sure how to do this one.
d. I think 1/n^p diverges when p<1. For p<1, 2p<2 so 1/n^2p < 1/n^2 which is a convergent series. So my p is correct. Am I right ?