## AmTran_Bus one year ago Someone check this calc 2?

1. AmTran_Bus

2. AmTran_Bus

I said converges since I got a limit at 0?

3. Haseeb96

Correct

4. freckles

how did you get 0?

5. freckles

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

6. AmTran_Bus

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

7. AmTran_Bus

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

8. freckles

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

9. freckles

not 0

10. AmTran_Bus

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

11. freckles

infinity or -infinity means it diverges

12. Haseeb96

if the limit is infinity then it will be divergence

13. freckles

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

14. Haseeb96

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

15. freckles

why is the limit 0 @Haseeb96

16. AmTran_Bus

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

17. freckles

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

18. freckles

do you understand why it diverges @AmTran_Bus

19. AmTran_Bus

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

20. AmTran_Bus

But I see what you are saying with that @freckles

21. 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.

22. AmTran_Bus

Thanks solomon

23. SolomonZelman

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

24. freckles

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

25. SolomonZelman

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

26. AmTran_Bus

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

27. AmTran_Bus

Thanks solomonzelman

28. SolomonZelman

yw

29. SolomonZelman

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

30. SolomonZelman

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