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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Determine whether the geometric series is convergent or divergent. 8 + 7 + 49/8 + 343/64 + …
Solution:
In the geometric series 8 + 7 + 49/8 + 343/64 + …
a = first term = 8
So the ratio r of a term and its preceding term is = 7/8 = (49/8)/7 = (343/64)/(49/8) = 7/8 = 0.875
It is a geometric series.
In this case, |r| < 1 the series is convergent and the sum of an infinite geometric series is written as a/(1 - r)
Substituting the values
= 8/(1 - 0.875)
By further calculation
= 8/0.125
= 64
Therefore, the geometric series is convergent.
Determine whether the geometric series is convergent or divergent. 8 + 7 + 49/8 + 343/64 + …
Summary:
The given geometric series 8 + 7 + 49/8 + 343/64 + … is convergent.
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