Question

Determine whether the series [infinity] 4 n0.64 n = 1 is convergent or divergent.

1) Convergent
2) Divergent

Answer 1

To determine whether the series ∑ 4n*0.64^n is convergent or divergent, we can use the ratio test. The absolute value of the ratio of consecutive terms in the series is 4, which is a finite number. Therefore, the series is convergent.

Step-by-step explanation:

To determine whether the series ∑ 4n*0.64^n is convergent or divergent, we can use the ratio test. The ratio test states that if the absolute value of the ratio of consecutive terms approaches a finite number as n approaches infinity, the series is convergent. If the absolute value of the ratio of consecutive terms approaches infinity, the series is divergent.

Let's apply the ratio test to our series:

|(4(n+1)*0.64^(n+1))/(4n*0.64^n)|

= |(4*0.64)/(0.64)| = |4|

The absolute value of the ratio is a finite number (4), therefore the series is convergent.