Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Does the series converge or diverge? If it converges, what is the sum? Show your work.
∑∞ n=1 - 4(-1/2)^n-1

Answer 1

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. The sum of the reciprocals of two consecutive even integers is
9/40.This can be represented by the equation shown.
1/x + 1/x+2 = 9/40
Use the rational equation to determine the integers. Show all work.

Answer 2

AAAaannndd the bot gets it wrong yet again!
You say that r=2; if that were true, the series would diverge, since |r| > 1.

You have a geometric series with
a = 2
r = -1/2
so the sum is a/(1-r) = 2/(3/2) = 4/3

Answer 3

For the other problem, you got the right answer in spite of bogus calculations.

1/x + 1/(x+2) = 9/40
x+2 + x = 9/40 x(x+2)
80x+80 = 9x^2+18x
9x^2-62x-80 = 0
(x-8)(9x+10) = 0
x = 8 or -10/9
we want an integer, so pick x=8