Question

Determine the Convergence or Divergence of the sequence with the given n- th term. If the converges find the limit.

a.) a_{n}= (-3/7)^{n}+4

b.) a_{n}= nsin(1/n)

c.) a_{n}= cos n?

Answer #1

1. Determine the convergence or divergence of the sequence with
given ??h term
(a) an=4-5/(n^2+1)
(b) an= 1/√?
(c) an= (sin√?)/ √?

For Xn given by the following, prove the convergence
or divergence of the sequence (Xn) with a formal proof,
clearly and neatly:
a) Xn = n2/(2n2+1)
b) Xn = (-1)n/(n+1)
c) Xn = sin(n)/(n2+1)

Determine the convergence/divergence of the following series
using the integral test:
a.) ∑= (1)/n(In(n))^2 (Upper limit of sigma is ∞ ,and the lower
limit of sigma is n=2)
b.) ∑ (n-4)/(n^2-2n+1) (Upper limit of sigma is ∞ and the lower
limit of the sigma is n=2
c.)∑ (n)/(n^2+1) (Upper limit of sigma ∞ and the lower limit
sigma is n=1)
d.) ∑ e^-n^2 (Upper limit of sigma ∞ and the lower limit sigma
is n=1)

Using the definition of convergence of a sequence, prove that the
sequence converges to the proposed limit.
lim (as n goes to infinity) 1/(n^2) = 0

Use the Monotone Convergence Theorem to show that each
sequence
converges.
a)an= -(2/3)^n
b)an= 1+ 1/n
c) 2/(-n)^2

1. Find the limit of the sequence whose terms are given by an=
(n^2)(1-cos(5.6/n))
2. for the sequence an= 2(an-1 - 2) and a1=3
the first term is?
the second term is?
the third term is?
the forth term is?
the fifth term is?

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

Test the series for convergence or divergence.
∞
(−1)n
8n − 5
9n + 5
n = 1
Step 1
To decide whether
∞
(−1)n
8n − 5
9n + 5
n = 1
converges, we must find lim n → ∞
8n − 5
9n + 5
.
The highest power of n in the fraction is
1
1
.
Step 2
Dividing numerator and denominator by n gives us lim n
→ ∞
8n − 5
9n +...

Determine the convergence or divergence if each integral by
using a comparison function. Show work using the steps below:
A. Indicate the comparison function you are using.
B. Indicate if your comparison function is larger or smaller
than the original function.
C. Indicate if your comparison integral converges or diverges.
Explain why.
D. State if the original integral converges or diverges. If it
converges, you don’t need to give the value it converges to.
11. integral from 1 to infinity...

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