Question

converges or diverges and for what reason? (n!)/9^(n+1)

Answer #1

**Ratio test:-**

If the series is defined as,

Then, the limit,

- If L<1, then the series is absolutely convergent and hence
convergent.
- If L>1, then the series is divergent.
- If L=1, then the series may be conditionally convergent, absolutely convergent or divergent.

Determine whether the limit converges or diverges, if it
converges, find the limit.
an = (1+(4/n))^n

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

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

Determine whether the following series converges or
diverges:∞∑n=1 ln(1 +1/n).

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

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

Determine whether the series
∞
∑
n=1
(e^n+1+ (−1)^n+1)/(π^n)
converges or diverges. If it is convergent, find its
sum.

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

Explain why the series converges or diverges:

Explain why the series converges or diverges:

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