Question

find the sum of the infinite geometric series -8+4-2+1-

Answer 1

\[-8+4-2+1-\cdots~~?\]

Answer 2

Each successive term has an alternating sign and is half of the previous term, making the common ratio \(-\dfrac{1}{2}\).

The sum of an infinite geometric series \(\displaystyle\sum_{k=0}^\infty a\times r^k=\frac{a}{1-r}\) for \(|r|<1\).

Answer 3

common factor r is -1/2
so by infinite GM formula of a/(1-r)=-8/(1-(-1/2))=-8/(3/2)=-16/3

Answer 4

so how would you show work for this and show your steps to finding the answer?

Answer 5

the first term = a = -8
and common ratio = r = -0.5

sum to infinity = a / (1 - r)

so plug a = 8 and r -= -0.5 into the above formula