Determine whether the geometric series is convergent or divergent. 
10 + 9 + 81/10 + 729/100 +…. If it is convergent, find its sum.

Solution:

Given: Geometric series is 10 + 9 + 81/10 + 729/100 +….

The given series looks like to be in geometric progression with constant ratio r

r = 2nd term/1st term = a₂/a₁

= 9/10

We know that if the ‘r’ is less than 1 then it is convergent

Here 9/10 < 1, it 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 = 10/(1-9/10)

= 10/(1/10)

Sum = 100

Therefore, the given series is convergent and its sum is 100.

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Determine whether the geometric series is convergent or divergent. 
10 + 9 + 81/10 + 729/100 +…. If it is convergent, find its sum.

Summary:

The geometric series is convergent or divergent 10 + 9 + 81/10 + 729/100 +…. It is convergent and its sum is 100.