Question

Explain why each sequence diverges:

{cos nπ}

{1+(-1)^n}

{sqrt(n)}

Answer #1

Use the Divergence Criterion to prove that the sequence an =
(−1)n + 1 n diverges.

Determine whether the sequence a_n = (3^n + 4^n)^(1/n) diverges
or converges

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))

I know that sequence cos(1/n) is bounded but how to show that
the sequence {cos(1/n) is also monotonic
Please write clearly

Problem 6. Show that the following sequence diverges: an
=10+(−1)^n x n/(n+10)

determine whether the sequence converges or diverges.
a_n=(-1)^n n+7/n^2+2

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

State whether the given series converges or diverges, and
why.
#21 sum 1/n^5, n=1 to infinity
#22 sum 1/5^n, n=0 to infinity
#23 sum 6^n / 5^n, n=0 to infinity
#24 sum n^-4, n=1 to infinity
#25 sum sqrt(n), n=1 to infinity

Why we can let sequence an=1/2n(pi) to be a sequence of function
2xsin(1/x)-cos(1/x)??? Please explain it.

Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1
= sqrt(3a_n) for n ≥ 1. we know that the sequence converges. Find
its limit.
Hint: You may make use of the property that lim n→∞ b_n = lim
n→∞ b_n if a sequence (b_n)∞n=1 converges to a positive real
number.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 16 minutes ago

asked 16 minutes ago

asked 21 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago