Someone check this calc 2?

- AmTran_Bus

Someone check this calc 2?

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- AmTran_Bus

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- AmTran_Bus

I said converges since I got a limit at 0?

- Haseeb96

Correct

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## More answers

- freckles

how did you get 0?

- freckles

\[\lim_{n \rightarrow \infty}n(n-6)\]
that looks like a product of really big numbers

- AmTran_Bus

Did i mess up? let me try again...

- AmTran_Bus

@Haseeb96 @freckles so am i right or not guess we can check on wolfram

- freckles

the product of really big positive numbers is a really big positive number

- freckles

not 0

- AmTran_Bus

So the limit is infinity? I mean, as long as there is a limit it converges, right?

- freckles

infinity or -infinity means it diverges

- Haseeb96

if the limit is infinity then it will be divergence

- freckles

infinity isn't a number just so you know
it just means it gets really really big

- Haseeb96

but @freckles he said limit is 0
so i said he is correct

- freckles

why is the limit 0 @Haseeb96

- AmTran_Bus

Ok. Well, thanks all. I need to go back and review I guess.

- freckles

I'm pretty sure the product of really big positive numbers can not be 0

- freckles

do you understand why it diverges @AmTran_Bus

- AmTran_Bus

Yes, I understand if it is infinity it diverges. Thanks. But I need to solve the limit correctly.

- AmTran_Bus

But I see what you are saying with that @freckles

- SolomonZelman

\(a_n=n(n-6)\)
\(\displaystyle \lim_{n\rightarrow\infty }n(n-6)\)
\(\displaystyle \lim_{n\rightarrow\infty }n^2-6n\)
diverges to positive inifinity.

- AmTran_Bus

Thanks solomon

- SolomonZelman

Sure.... everytime to see the sequence convergence, for any sequence \(A_n\) , take the limit of it as n approaches infinity

- freckles

60(54)=?
100(94)=?
1000(994)=?
10000(9994)=?
these products are getting super super big

- SolomonZelman

And if sequence diverges, then (always!) the series diverges

- AmTran_Bus

Yes. I super see that now. Thanks so much freckles. I think I understand it.

- AmTran_Bus

Thanks solomonzelman

- SolomonZelman

yw

- SolomonZelman

((that was my favorite section when I learned it, btw))

- SolomonZelman

good luck, you will get an A I am sure... !

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