Question

Determine whether the following sequences converge or diverge. If a sequence converges, find its limit. If a sequence diverges, explain why.

(a) *a _{n} =* ((-1)

(b) *a _{n} = (*sin(3n))/(1- sqrt(n))

Answer #1

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

Use L’Hopital’s Rule to determine if the following sequences
converge or diverge. If the sequence converges, what does it
converge to?
(a) an = (n^2+3n+5)/(n^2+e^n)
(b) bn = (sin(n −1 ))/( n−1)
(c) cn = ln(n)/ √n

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)

Determine whether the sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.)
an = (4^n+1) /
9^n

Determine whether the sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.)
an = 4 − (0.7)n
lim n→∞ an =
please box answer

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/nn from 0 to infinity
c) sum of (-1)n /(1 + 1/n) from 0 to infinity
d) sum of 1/5n from 0 to infinity

1) Determine if the sequence converges or Diverges. If it
converges find the limit.
an=n2*(e-n)

Determine whether the limit converges or diverges, if it
converges, find the limit.
an = (1+(4/n))^n

Use the ratio test to determine whether∑n=12∞n2+55n
converges or diverges.
(a) Find the ratio of successive terms. Write your
answer as a fully simplified fraction. For n≥12,
limn→∞∣∣∣an+1an∣∣∣=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞
as infinity and −∞ as -infinity. If the limit does
not exist, enter DNE.
limn→∞∣∣∣an+1an∣∣∣ =
(c) By the ratio test, does the series converge,
diverge, or is the test inconclusive?

Explain whether the following integrals converge or not. If the
integral converges, find the value. If the integral does not
converge, describe why (does it go to +infinity, -infinity,
oscillate, ?)
i) Integral from x=1 to x=infinity of x^-1.4 dx
ii) Integral from x=1 to x=infinity of 1/x^2 * (sin x)^2 dx
iii) Integral from x=0 to x=1 of 1/(1-x) dx

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