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

nicekikah 2021-11-03 Answered
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 3-4+16/3-64/9+........

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Faiza Fuller
Answered 2021-11-04 Author has 18760 answers
The given question already states that this is a geometric series.
A geometric series is convergent if and only if its common ratio r satisfies the following inequality
|r|
In the given problem, we have
\(\displaystyle{r}={\frac{{{a}_{{{2}}}}}{{{a}_{{{1}}}}}}={\frac{{-{4}}}{{{3}}}}\)
Since the absolute value of the common ratio is \(\displaystyle{\frac{{{4}}}{{{3}}}}\approx{1.33}\), which is not less than 1, the given geometric series is divergent.
Results:
divergent because the common ratio is not less than 1.
Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...