## sloppycanada one year ago I'm so confused on this, I'm not sure what I'm supposed to use for any of this, I don't know the common denominator or anything. Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1. http://imgur.com/BaADfyq

1. ganeshie8

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

So T6 is -62,500?

3. ganeshie8

first term, $$\large t_1 ~=~-4$$ second term, $$\large t_2 ~=~-4*5 = -20$$ third term, $$\large t_3 ~=~-20*5 = -100$$ keep going till the 6th term

4. ganeshie8

-62,500 is wrong

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

6. ganeshie8

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

8. ganeshie8

Good!

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

10. ganeshie8

look at the terms : $-4,~~-20,~~-100,~~-500,~~-2500,~~ \ldots$ what do you notice ? do they seem to converge to some number ?

You could go on for ever without getting a sum.

12. ganeshie8

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

So for an equation like this - Find the sum of the infinite series 3 + 1.2 + 0.48 + 0.192 + ...if it exists. All I would do is use the formula to find the equation of the infinite series?

14. ganeshie8

what kind of series is it, geometric/arithmetic ?

Geometric?

16. ganeshie8

there is a nice criterion for testing convergence of geometric series, you simply look at the common ratio

17. ganeshie8

whats the common ratio of given series ?

The equation is tn/(tn-1)

Common ratio is 2.5

20. ganeshie8

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

21. ganeshie8

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

22. ganeshie8

try again

.4?

24. ganeshie8

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

25. ganeshie8

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

26. ganeshie8

use infinite sum formula to find the sum

27. ganeshie8

do you have the formula wid u ?

S(infinite) = 3/t-.4

I have it in my notes

30. ganeshie8

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

31. ganeshie8

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

32. ganeshie8

simplify

5?

34. ganeshie8

Yes!

I have three more if you have time?

36. ganeshie8

okay il try, post

38. ganeshie8

Firs test if the series converges by finding the common ratio

39. ganeshie8

whats the common ratio ?

1.33?

41. ganeshie8

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

42. ganeshie8

we say the sum does not exist

Okay so the answer would be "No solution"

44. ganeshie8

As you can see, the common ratio decides whether an infinite converges to some number, or if it diverges

45. ganeshie8

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?

47. ganeshie8

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

49. ganeshie8

Yes, when you multiply the first term by 1.33, you get a bigger next term; the terms keep growing and the sum wont reach a specific number

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

51. ganeshie8

how did u get 0.498 ?

52. ganeshie8

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

I didn't round.

54. ganeshie8

me neither could you show ur work please

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

56. ganeshie8

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

57. ganeshie8

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?

59. ganeshie8

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

60. ganeshie8

1/2 = 0.5 both are exact

61. ganeshie8

1/3 = 0.33333333333333333333333333... clearly the decimal wont be exact because you can't write out infinitely many 3's

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

63. ganeshie8

$\huge \color{red}{\checkmark}$

Ah hah! Thank you!

Not sure how to show my appreciation on this site (if there are points or something), but let me know if there is.

66. ganeshie8

67. ganeshie8

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

68. ganeshie8

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

70. ganeshie8

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

71. ganeshie8

how did u get 49.140 ?

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

|dw:1435126030016:dw|

74. ganeshie8

why are you multiplying by 2 ?

75. ganeshie8

first term is 1 right

76. ganeshie8

|dw:1435126092819:dw|

Okay so it'd just be 4095

78. ganeshie8

Correct.