Determine whether the geometric series is convergent or divergent. If it is conv

vazelinahS 2021-11-02 Answered
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
102+0.40.008+
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Expert Answer

unessodopunsep
Answered 2021-11-03 Author has 105 answers

Geometric series:
n=0arn=a1r
Where r and a are constants
If |r|<1, then the series converges to a1r
102+0.40.08
10+10(15)+10(15)2+10(15)3
n=010(15)n
This is a geometric series with common ration r=15 and Initial Term a=10
Since |r|=15<1, the given geometric series converges.
Sum of the geometric series is
S=a1r=101(15)=101+15=1065=506=253
The series converges to 253

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