Kenneth S. answered • 05/01/16
Tutor
4.8
(62)
Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
∞
∑ (-1)n (8/5n) = 8•[ -1/5 + 1/25 - 1/125 + ...] = 8 times the sum of an infinite geometric series
n=1
that has a = -1/5 and r = -15 also.
The sum of said infinite series = a/(1-r) = (-1/5) / (1+1/5) = (-1/5)•(5/6) = -1/6.
Multiplying this sum by 8 to get the final answer, we have -4/3.
Kenneth S.
Well, let's see. I factored out the 8, and then I expanded the first few terms. Observe that the first term is negative, and the second term is positive,since the power on (-1) are 1 and 2 for the first two terms. Therefore the first two terms have a negative total. Then the 3rd and 4th terms are, respectively, negative and positive, also [since we have an alternating series), and their total is also negative. Et cetera, et cetera, et cetera. So the answer has to be 8 times a negative.
I'm sticking with my answer, based on how you wrote the general (nth) term, and the n=1 starting value under the Sigma. Keep me informed on how the teacher likes this analysis.
Report
05/01/16
Aubree S.
05/01/16