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) 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.
#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...
Find the radius of convergence, R, of the series. Find
the interval, I, of convergence of the series. (Enter your
answer using interval notation
∞
(−1)n
(x −
4)n
3n +
1
n = 0
∞
(x −
4)n
n7 + 1
n = 0
∞
7n (x +
5)n
n
n = 1
∞
(x −
13)n
nn
n = 1
∞
4nxn
n2
n = 1