Question

How do you use the ratio test to first find the ratio of convergence and then the interval of convergence for this series?

Answer #1

Use the ratio test to determine convergence or divergence. If
the ratio test is inconclusive, use another method to determine
convergence or divergence.
∞
(−1)n(n!)2
/
(7n)!
n = 1
Its the series from 1 to infinity of
(-1)^n times (n!)^2 divided by (7n)!

1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use
the P-test. (You could also use the Integral Test, as is the case
with all series of this type.) According to the P-test:
∞∑k=1 1/5√k^3 converges
the P-test does not apply to ∞∑k=1 1/5√k^3
∞∑k=1 1/5√k^3 diverges
Now compute s4, the partial sum consisting of the first 4 terms
of ∞∑k=1 1 /5√k^3:
s4=
2. Test the series below for convergence using the Ratio
Test.
∞∑n=1 n^5 /1.2^n...

For the next two series, (1) find the interval of convergence
and (2) study convergence at the end points of the interval if any.
Also, (3) indicate for what values of x the series converges
absolutely, conditionally, or not at all. You must indicate the
test you use and show the interval of convergence both analytically
and graphically and summarize your results on the picture.
∑∞ n=1 ((−1)^n−1)/ (n^1/4)) *x^n

1. To test this series for convergence
∞∑n=1 n /√n^3+1
You could use the Limit Comparison Test, comparing it to the series
∞∑n=1 1 /n^p where p=
2. Test the series below for convergence using the Ratio
Test.
∞∑n=1 n^5/0.5^n
The limit of the ratio test simplifies to lim n→∞|f(n)| where
f(n)=
The limit is:

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

How do you find the power series representation and radius of
convergence for g(x) = 6 / (3+x)^3 ? thanks

how do find the radius of convergence?

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

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)

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