Question

Prove that a sequence (u_{n} such that n>=1)
absolutely converges if the limit as n approaches infinity of
n^{2}u_{n}=L>0

Answer #1

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

Let f be defined on the (0,infinity). Prove that the limit as x
approaches infinity of F(x) =L if and only if the limit as x
approaches 0 from the right of f(1/x) = L. Does this hold if we
replace L with either infinity or negative infinity?

Determine if the series converges conditionally, converges
absolutely, or diverges.
/sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4)
/sum(n=1 to infinity) sin(4n)/4^n

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

Prove that 5 | Un if and only if 5|n. Where Un is the Fibonacci
sequence.

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 if a sequence is a Cauchy sequence, then it
converges.

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

Suppose {xn} is a sequence of real numbers that converges to
+infinity, and suppose that {bn} is a sequence of real numbers that
converges. Prove that {xn+bn} converges to +infinity.

Consider the series ∑n=1 ∞ an
where
an=(5n+5)^(9n+1)/
12^n
In this problem you must attempt to use the Ratio Test to decide
whether the series converges.
Compute
L= lim n→∞
∣∣∣an+1/an∣∣
Enter the numerical value of the limit L if it converges, INF if
the limit for L diverges to infinity, MINF if it diverges to
negative infinity, or DIV if it diverges but not to infinity or
negative infinity.
L=
Which of the following statements is true?
A. The...

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