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ok, your common ratio is>?

Okay

your common ratio is not "okay" lol

do you know what a common ratio is?

XD Oh I thought you were telling me that, I'm sorry. I do not know what a common ratio is.

common ratio, is a number by which you multiply to get to the next term each time.

Oh okay so would it be (-1/6)?

Okay! I undertsand that!

Do you know what it means for a series to converge and for a series to diverge?

oh, for a sequence to diverge and converge

No I do not, that's what I'm coversed on. My lesson never went over it :(

confused**

Ohhhhhh that makes sense okay

What about if something diverges?

So the more terms you take, the close and close you approach what value?

0, since the number values get smaller and smaller

yes, that is correct

So that means that "sequence converges to zero"

^-^ Thanks a lot that makes sense!

And you asked about divergence, i will answer that now

When I do reach series in my lesson I will come to you! and yes

Say you got
1, 2, 4, 8, 16, 32 .......
what is the pattern here, can you tell me?

the next number is being multiplied by 2

yes, r=2

Yes!

that means that sequence diverges.

yes, what you said is correct

that is a good definition of convergence of a SEQUENCE.

Okay only for a sequence, got it.

now, a series is the sum of terms in a sequence.

is this making some sense?

I believe so, yes

yes, so for example in your case, your sequence converges to what?

The sequence converges to zero

yes

But in this case, the rule does not apply

this rule always applies
provided that ratio is: -1

and so it is in your case, cuz r=-1/6
so it is between -1 and 1

Oh okay, I was thinking 0 was r, but r is the common ratio which was -1/6, That makes sense

lets see, but why does the common ratio r has to satisfy -1

Makes sense

so, if r\(\ge\)1
or if r\(\le\)-1
then the \(\large\color{black}{ \displaystyle r^{\infty -1}}\) part will go to either ∞ or -∞.
but if -1

Anytime!