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.
A day full of math games & activities. Find one near you.
Determine whether the geometric series is convergent or divergent.
9 + 8 + 64/9 + 512/81 +…. If it is convergent, find its sum?
Solution:
Given: Geometric series is 9 + 8 + 64/9 + 512/81 +….
The given series looks like to be in geometric progression with constant common ratio r
r = 2nd term/1st term = a2/a1
= 8/9
We know that if the ‘r’ is less than 1 then it is convergent
Here 8/9 < 1.
So, the series is convergent.
Clearly, this is the sum of an infinite geometric series.
sum of GP = a/(1 - r)
Where a is the first term, 4 is the common ratio.
Sum = 9/(1-8/9)
= 9/(1/9)
Sum = 81
Therefore, the given series is convergent and its sum is 81.
Determine whether the geometric series is convergent or divergent.
9 + 8 + 64/9 + 512/81 +…. If it is convergent, find its sum?
Summary:
The geometric series 9 + 8 + 64/9 + 512/81 +…. is convergent and its sum is 81.
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