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.) a n = n 3 /n + 2

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 limit comparison test to determine whether the series Σ∞
n=1 (2^n)/(3+4^n) converges or diverges. Show your work. What
series did you use for the comparison? How did you figure out the
behavior (converge or diverge) of the series that you used for the
comparison?

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