Question

Please help! Find the value of the convergent series:

Answer 1

2.25

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

`Σ3( - (1)/(3) ) {}^(n - 1)`

Since we can represent this a summation series, we can use that convergent value is equal to

`(a _(1) )/(1 - r)`

where a1 is initial term and r is common ratio.

R is -1/3

A1 is 3.

`(3)/(1 - ( - 1)/(3) ) = (3)/( (4)/(3) ) = 2.25`

So the answer is 2.25