1) Find the radius of convergence and interval
of convergence of the given series Σ x^2n/n!
2) Find the power series representation of
f(x)=(x-1)/(x+2) first then find its interval of convergence.
find the radius of convergence and interval of convergence of
the series ∑ n=1 ~ ∞ (3^n)((x+4)^n) / √n
Please solve this problem with detailed process of solving.
I can't understand why the answer is [-13/3, -11/3)
I thought that the answer was (-13/3, -11/3].
Can you explain why that is the answer?
1. expand each function in a Taylor Series and determine radius
of convergence.
a) f(x) = 1/(1-x) at x0 = 0
b) f(x) = e^(-x) at x0 = ln(2)
c) f(x) = sqrt(1+x) at x0 = 0
#13) Find the radius and interval of convergence of the power
series (Sigma∞ n=1) (−1)^n(x − 1)^n/n4^n by responding to the
following sequence of questions.
(a) Compute the limit L = lim n→∞ |an+1|/|an| .
(b) Given that the power series absolutely converges for L <
1 by the Ratio Test, compute the radius of convergence, where the
radius of convergence is the real number R such that the power
series converges for all |x| < R.
(c) Test whether...