AboutSteve Holleran Expertise I can help with all math questions from basic math to Calculus.
Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.
Experience 33 years teaching experience in NJ public schools
Education/Credentials B.S. Mathematics : Wake Forest University 1972
M.S. Mathematics : Monmouth University 1981
Question Hi, I have a math test tomorrow and there is a question on my review sheet
that I just can't figure out, here's the question
For the geometric series, find the sum. If the series has no sum, say so.
1/2-1/3+2/9-4/27+..
If you could explain how to do it, that would be great!
Thank you,
Jess
Answer Hi Jess,
Okay, an infinite geometric series will have a sum if the ratio (r) between successive terms is between -1 and 1 (another way of saying this is if its absolute value is between 0 and 1).
Here, you can find the ratio by dividing any two neighboring terms.
Lets say you took the second and third ones:
(2/9) / (-1/3) = (-2/3) = r
so, this series has a sum.
Now, the formula for the sum of an infinite geometric series is
S = a / (1 - r) where a is the first term
and r is the common ratio.
So, here we have:
S = (1/2) / (1 - (-2/3))
= (1/2) / (5/3) = 3/10
And this would be the sum of the series.
By the way, if the ratio is ever more than 1 or less than -1, then the infinite series has no sum (and is called divergent).
