Question

prove whether the following series converge absolutely, converge conditionally or diverge give limit

a) sum of (-5)^{n} /n! from 0 to infinity

b) sum of 1/n^{n} from 0 to infinity

c) sum of (-1)^{n} /(1 + 1/n) from 0 to infinity

d) sum of 1/5^{n} from 0 to infinity

Answer #1

Determine whether the following sequences converge or diverge.
If a sequence converges, find its limit. If a sequence diverges,
explain why.
(a) an = ((-1)nn)/
(n+sqrt(n))
(b) an = (sin(3n))/(1- sqrt(n))

Do the following sequences converge or diverge? If it converges,
find its limit.
a) an = (4n^3+3n-6) / (5n^26n+2)
b) an = (3n^3+2n-6) / (4n^3+n^2+3n+1)
c) an = (n sin n) / (n^2+4)
d) an = (1/5)^n

Determine if the series converges conditionally, converges
absolutely, or diverges.
/sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4)
/sum(n=1 to infinity) sin(4n)/4^n

Prove whether or not the series converges
a) sum of ( 6n2 + 89n +73)/(n4 - 213n)
from 1 to infinity
b) sum of 1/(n3 +2) from 0 to infinity
c) sum of n1/n from 1 to infinity
d) sum of (-1)n /ln(n) from 2 to infinity (why we
start with 2 instead of 1?)

Given the alternating series:
sigma(2 to infinity): (-1)^n / ln n
Determine if the series converge
absolutely. (Use the fact
that: ln n <
n)
Determine if the series converge
conditionally.
(Estimate the sum of the infinite series using the
first 4 terms in the series and estimate the
error.
How many terms should we use to approximate the sum of
the infinite series in question, if we want the error to be less
than 0.5?

Determine whether the given series are absolutely convergent,
conditionally convergent or divergent: a.) sigma ∞to n=0 (−3)n\(2n
+ 1)!
b.) sigma ∞ ton=1 (2n)!\(n!)2

Determine whether the following sequences converge or diverge.
If it converges, ﬁnd the limit. Must show work
1.)an = nsin(1/n)
2.)an = sin(n)
3).an =4^n /1 + 9^n
4).an = ln(n+1) − ln(n)

Given the alternating
series:
n=2∞(-1)^n/ln(n)
(7 pts) Determine if the series converge
absolutely. (Use the fact
that: ln n <
n )
(7 pts) Determine if the series converge
conditionally.
(7 pts) Estimate the sum of the infinite series using
the first 4 terms in the series and estimate the
error.
(7 pts) How many terms should we use to approximate the
sum of the infinite series in question, if we want the error to be
less than 0.5?

Consider the series ∑n=1 ∞ an
where
an=(5n+5)^(9n+1)/
12^n
In this problem you must attempt to use the Ratio Test to decide
whether the series converges.
Compute
L= lim n→∞
∣∣∣an+1/an∣∣
Enter the numerical value of the limit L if it converges, INF if
the limit for L diverges to infinity, MINF if it diverges to
negative infinity, or DIV if it diverges but not to infinity or
negative infinity.
L=
Which of the following statements is true?
A. The...

Infinity Sigma n=1 (n+1 / n^7/3 + sqrt n)
Does this series converge or diverge?

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