Question

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)

Answer #1

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.

1) Find the radius of convergence, R, of the series and Find the
interval of convergence, I, of the series. (Enter your answer using
interval notation.)
∞
4nxn
n2
n = 1
2) Find the radius of convergence, R, of the series.
Find the interval of convergence, I, of the series. (Enter
your answer using interval notation.)
∞
(x −
4)n
n7 + 1
n = 0

1) Find the interval of convergence I of the series.
(Enter your answer using interval notation.)
∞
7n (x +
5)n
n
n = 1
2) Find the radius of convergence, R, of the following
series.
∞
n!(7x
− 1)n
n = 1
3) Suppose that the radius of convergence of the power
series
cn xn
is R.
What is the radius of convergence of the power series
cn x5n
?
4) Find the radius of convergence, R, of the...

Find the radius of convergence, R of the series. And find the
interval of, I, of convergence of the series.
The sum from n=1 to infinity: (4^n)(n^2)(x^n)

Find the radius of convergence, R, of the series.
∞
n
7n
(x + 3)n
n = 1
R =
Find the interval, I, of convergence of the series. (Enter
your answer using interval notation.)
I =

Find the radius of convergence and the interval of convergence
of the power series. (Please check endpoints) X∞ n=1 ((x −
2)n )/(n3n )

Find the radius of convergence, R, of the series.
∞
(x − 2)n
/n 3n
n = 0
R =
Find the interval, I, of convergence of the series. (Enter
your answer using interval notation.)
I =

find the radius of convergence, R, of the series.
Sigma n=1 to infinity x^n/(4^nn^5)
R=
Find the interval, I of convergence of the series.

Find the radius of convergence, R, of the series.
∞
n = 1
(−1)nxn
n2
R = ?
Find the interval, I, of convergence of the series. (Enter
your answer using interval notation.)
I = ?

Find the radius of convergence, R, of the series. ∞ n = 1 (x +
6)n / 6n ln(n)
and find the interval of convergence

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