Question

Write down a power series with interval of convergence (0, 4).

Write down a power series with interval of convergence [0, 4).

Answer #1

Consider The Power Series: ∞∑n=0 (2x)^n a)Find the radius of
convergence b)Find the interval of convergence

determine the interval of convergence of the power series ∑ ( 1
to ^ infinity) (n^4 x^n )/ 4^n

Find the interval of convergence for the power series
∑?=0∞ 8?(?−5)3?+1
Give your answer using interval notation. If you need to use ∞,
type INF. If there is only one point in the
interval of convergence, the interval notation is
[a]. For example, if 0 is the only point in the
interval of convergence, you would answer with [0].

Find a power series representation for the function; find the
interval of convergence. (Give your power series representation
centered at x = 0.) f(x) = (x2 + 1)/ (2x − 1)

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 interval of convergence of the power series. (Be sure
to include a check for convergence at the endpoints of the
interval. If the interval of convergence is an interval, enter your
answer using interval notation. If the interval of convergence is a
finite set, enter your answer using set notation.)
∞
(−1)n + 1(x − 3)n
n7n
n = 1

Find the interval of convergence of the power
series f ( x ) = ∑ n = 1 ∞ ( x + 3 ) n 2 n.

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

Evaluate integral 1/1+x^9 dx as a power series. Give the
interval of convergence of the power series.

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...

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