a = -4 is the first term r = -1/2 is the common ratio the reason why is because the expression -4(-1/2)^(n-1) is in the form a(r)^(n-1). Notice how -4 matches with the 'a'; the -1/2 matches with the r
The common ratio will determine if the infinite series converges or not. r = -1/2 leads to |r| = |-1/2| = 1/2 = 0.5 Since |r| < 1 (in this case 0.5 < 1) is true, this means the series does converge. Put another way, because r = -1/2 = -0.5 makes -1 < r < 1 true, the series converges.
Use the formula below to find the converging value S S = a/(1-r) S = -4/(1-(-1/2)) S = -4/(1+1/2) S = -4/(2/2+1/2) S = -4/(3/2) S = (-4/1)/(3/2) S = (-4/1)*(2/3) S = (-4*2)/(1*3) S = -8/3 The infinite series converges to -8/3 So the sum is -8/3
