Question

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

Answer #1

Let

We want

So that

Taking we have and for which we have

Meaning by the definition of limit

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

Mathematical Real Analysis
Convergence Sequence Conception Question:
By the definition: for all epsilon >0 there exists a N such
that for all n>N absolute an-a < epsilon
Question: assume bn ----->b and b is not 0. prove
that lim n to infinity 1/ bn = 1/ b .
Please Tell me why here we need to have N1 and N2 and
Find the Max(N1,N2) but other example we don't.
Solve the question step by step as well

suppose (Sn) converges to s and (tn) converges to t.
use the definition of convergence of sequences to prove that
(sn+tn) converges to s+t.

2. Sequence Convergence¶ (To be answered in LaTex)
Show that the following sequence limits using either an ?−?ε−δ
argument
a) lim (3?+1) / (2?+5) = 3/2 answer in LaTex
b) lim (2?) / (n+2) =2 answer in LaTex
c) lim [(1/?) − 1/(?+1)] = 0 answer in LaTex

Prove that if (xn) is a sequence of real numbers,
then lim sup|xn| = 0 as n approaches infinity. if and
only if the limit of (xN) exists and xn
approaches 0.

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 − (0.7)n
lim n→∞ an =
please box answer

Prove that if a sequence converges to a limit x then very
subsequence converges to x.

suppose that the sequence (sn) converges to s. prove that if s
> 0 and sn >= 0 for all n, then the sequence (sqrt(sn))
converges to sqrt(s)

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 +...

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