SOLUTION: Hello. Hoping you can help me answer this question. A) write geometric series -9/2+3/2-1/2+1/6...+1/39366 in summation notation. B)using the formula for the sum of an geometric ser

Algebra ->  Sequences-and-series -> SOLUTION: Hello. Hoping you can help me answer this question. A) write geometric series -9/2+3/2-1/2+1/6...+1/39366 in summation notation. B)using the formula for the sum of an geometric ser      Log On


   

Question 891682: Hello. Hoping you can help me answer this question. A) write geometric series -9/2+3/2-1/2+1/6...+1/39366 in summation notation. B)using the formula for the sum of an geometric series, compute the sum.
Here's what I know. The numerator is multiplied by 1/3 to get from each term to the next. The denominator decreases by 1 when comparing n=term #, n=1 to denom in -9/2, 2-1=1, n=2 in 3/2, 2-2=0 and so on. I see the pattern, just not sure how to write it. Also, when writing it in sn, I know my bottom starting amount will be n=1
Any help you can give would be appreciated. Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It looks like each successive number is multiplied by -1%2F3
2nd term : -%289%2F2%29%28-1%2F3%29=3%2F2
3rd term : %283%2F2%29%28-1%2F3%29=-1%2F2
4th term : -%281%2F2%29%28-1%2F3%29=1%2F6
So then, continuing on,
1%2F39366 would be the 12th term.
The constant term would be,
a%28-1%2F3%29=-9%2F2
a=27%2F2
So then, the series would look like,
A%5Bn%5D=%2827%2F2%29%28-1%2F3%29%5En
The sum would then be,
S%5Bn%5D=%28-9%2F2%29%28%28%281-%28-1%2F3%29%5En%29%29%2F%281-%28-1%2F3%29%29%29
S%5Bn%5D=%28-9%2F2%29%28%28%281-%28-1%2F3%29%5En%29%29%2F%284%2F3%29%29
S%5Bn%5D=%28-9%2F2%29%283%2F4%29%281-%28-1%2F3%29%5En%29
S%5Bn%5D=%28-27%2F8%29%281-%28-1%2F3%29%5En%29
So for n=12
S%5B12%5D=%28-27%2F8%29%281-%28-1%2F3%29%5E12%29
S%5B12%5D=%28-27%2F8%29%281-1%2F531441%29
highlight%28S%5B12%5D=-27%2F8%29