Question

Write out the first five terms of the sequence with {[(n+8)/n+1)]^n}^inf n=1 and find its limit as well as mention if it converges?

Answer #1

Find the point-wise limit and find out if the sequence converges
uniformly on [0,1] to its point-wise limit
1) (X^n)/(n)
2) (X^n)/(1-X^n)

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

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?

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))

In this task, you will write a proof to analyze the limit of a
sequence.
ASSUMPTIONS
Definition: A sequence {an} for n = 1 to ∞ converges
to a real number A if and only if for each ε > 0 there is a
positive integer N such that for all n ≥
N, |an – A| < ε .
Let P be 6. and Let Q be 24.
Define your sequence to be an = 4 +
1/(Pn +...

In this task, you will write a proof to analyze the limit of a
sequence.
ASSUMPTIONS
Definition: A sequence {an} for n = 1 to ∞ converges
to a real number A if and only if for each ε > 0 there is a
positive integer N such that for all n ≥
N, |an – A| < ε .
Let P be 6. and Let Q be 24.
Define your sequence to be an = 4 +
1/(Pn +...

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

Prove that a sequence (un such that n>=1)
absolutely converges if the limit as n approaches infinity of
n2un=L>0

1. Can a sequence attain its limit; that is, can the limit of a
sequence be one of the terms of the sequence? If so, give an
example. If not, explain.
2. If a sequence never attains its limit; could its terms
consist of a finite number of distinct values? If so, give an
example. If not, explain.

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.

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