At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

start with \(-4\), and keep multiplying by \(5\) to get the next term.

So T6 is -62,500?

-62,500 is wrong

Sorry, I did too many of them. -2500.

show me the work instead

T4 = -100 x 5 = -500
T5 = -500 x 5 = -2500
T6 = -2500 x 5 = -12500

Good!

And then how do I go about finding the sum of an infinite series?

You could go on for ever without getting a sum.

Yes, so we say the "sequence doesn't converge" and the infinite sum doesn't exist

what kind of series is it, geometric/arithmetic ?

Geometric?

whats the common ratio of given series ?

The equation is tn/(tn-1)

Common ratio is 2.5

yes work it
common ratio = (next term)/(present term)

looks you have worked it in reverse : (present term)/(next term)

try again

.4?

yes common ratio = 0.4 which is between -1 and 1
so the given series conveges

A geometric series converges if the common ratio is between -1 and 1

use infinite sum formula to find the sum

do you have the formula wid u ?

S(infinite) = 3/t-.4

I have it in my notes

\[\large S_{\infty} ~=~\dfrac{t_1}{1-r}\]

\[\large S_{\infty} ~=~\dfrac{3}{1-0.4}\]

simplify

5?

Yes!

I have three more if you have time?

okay il try, post

http://gyazo.com/f47f214fcdb2adb56c90ca6794e3f48d

Firs test if the series converges by finding the common ratio

whats the common ratio ?

1.33?

Yes, which is "not" in between -1 and 1
so the series does not converge.

we say the sum does not exist

Okay so the answer would be "No solution"

Answer would be "does not converge"

If it converges then it has a sum, if it does not converge there is not really a solution?

yes, do you see why the common ratio of 1.33 gives a diverging sum ?

Because it's larger then 1? and not between that -1 and 1

So for this problem - http://gyazo.com/15138c898cca305ec43a79e298d55821
The answer would be .498

how did u get 0.498 ?

im asking because im getting a more nice looking number : 0.5

I didn't round.

me neither
could you show ur work please

\[S \infty = \frac{ 1 }{ 3 }\div 1-.33\]

Ahh okay, you're rounding 1/3 to 0.33

i worked it like this :
\[\large S_{\infty}~=~\dfrac{1/3}{1-1/3} = \dfrac{1}{3-1}=\dfrac{1}{2}=0.5\]

I'm not sure why I changed from a fraction to a decimal. Fractions are more precise aren't they?

Yep
Fractions are exact
decimals are not so exact when you get a repeating decimal

1/2 = 0.5
both are exact

Okay, last one - http://gyazo.com/50d340d91d94093d361677d900fa46ee
Answer is 1.

\[\huge \color{red}{\checkmark}\]

Ah hah! Thank you!

yw! click the "Best Response" button next to any reply if you find the answer helpful

you could also write a testimonial if you think the helper is amazing

not encouraging you to write a testimonial for me right now, but just letting you know :)

Finding the sum of an geometric Find S12 for the series 1 + 2 + 4 + 8 +... like this is 49,140

go through this when u have time to know more about the site
http://openstudy.com/code-of-conduct

how did u get 49.140 ?

Sorry it should be 8,190.
2((1-2^12)/(1-2)) = 8190

|dw:1435126030016:dw|

why are you multiplying by 2 ?

first term is 1 right

|dw:1435126092819:dw|

Okay so it'd just be 4095

Correct.