Question

What is the sum of the infinite geometric series?

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Answer 1

1/2+ 1/4,+ 1/8, e2020 answer

Explanation:

Answer 2

You haven't provided the series, therefore, I can only help with the concept.

For an infinite geometric series, we have two possibilities for the common ratio (r):
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series

In an infinite series with r < 1, the summation can be found using the following rule:
sum =
`(a_(1) )/(1-r)`
where:
a₁ is the first term in the series
r is the common ratio

Example:
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =
`(2)/(1-0.5) = 4`

Hope this helps :)