Answer:
2.25
Step-by-step explanation:
Notice how the common ratio is -1/3, which means the series passes part 1 of the convergence test because -1/3 is in between -1 and 1.
We can also represent this as a summation series of
[tex]Σ3( - \frac{1}{3} ) {}^{n - 1} [/tex]
Since we can represent this a summation series, we can use that convergent value is equal to
[tex] \frac{a _{1} }{1 - r} [/tex]
where a1 is initial term and r is common ratio.
R is -1/3
A1 is 3.
[tex] \frac{3}{1 - \frac{ - 1}{3} } = \frac{3}{ \frac{4}{3} } = 2.25[/tex]
So the answer is 2.25
