Question

What is divergent and convergent>>>
only lim--->(infinite)=0 - (convergent)
if lim---> >(infinite) not zero (divergent)

Answer 1

I could help you if I knew what you meant.

Answer 2

If \[ \large
\lim_{n \to \infty } a_n \neq 0
\]Then it is divergent. Otherwise it's inconclusive.

Answer 3

what is inconclusive.. out from monotonic>>

Answer 4

\[\lim_{n \rightarrow 0}a_n=0\]
Is a REQUIREMENT for a series to converge. It is not SUFFICIENT. This means that if it is NOT equal to zero then it must diverge but it does not imply it must converge if it IS zero.

Answer 5

\[\lim_{n \rightarrow \infty}a_n=0\]

Answer 6

Is what it should read.

Answer 7

Consider \(1/n\). It's divergent yet it's infinite term is 0.

Answer 8

Ahh, so the divergence tests for if a series diverges. It can only tell you for certain that it diverges, but it can't tell you that it converges.

See, the reasoning is that if you take the limit of the series as it approaches infinity, it's like looking at the "final" term. So if the final term is anything bigger than 0, you know it diverges.

See, if the final term is anything, be it 1/2, 1, 3, or whatever that's not 0, then it means that the "final" term is not 0. Since we're talking about infinity here and there's no actual final term, then if it's something like 1, that means you're continually adding 1+1+1+1+... forever and never converging.

At least that's my intuition on the subject.

Answer 9

What is the question?

Answer 10

Determine the following series:::::
\[\sum_{n=1}^{\infty}(-1)\frac{n!^{2} 3^n }{(2n+1)! }\]

Answer 11

@abb0t
@Kainui

Answer 12

Determine what it is, or determine if it converges or not?

Answer 13

Use the ratio test. It's the best you can use when there are factorials.

Answer 14

converge absolutely,converge conditionally or divergent

Answer 15

Ratio test states:
\[L = \lim_{n \rightarrow ∞} \left| \frac{ a_{n+1} }{ a_n } \right|\]
if L < 1 the series is absolutely convergent (and hence convergent).
if L > 1 the series is divergent.
if L = 1 the series may be divergent, conditionally convergent, or absolutely convergent. (use different test)