Question

Consider the series ∑ n=1[infinity](3n)!28 n (n!) 3 . Let a n = (3n)!28 n (n!) 3 . When applying the ratio test to this series:

(a) Find the ratio a / n+1​

​
.

Answer 1

The student needs help applying the ratio test to the series ∑(3n)!/28ⁿ (n!)^3. The ratio an+1/an involves factorial and power manipulation.

Step-by-step explanation:

The student is asking for assistance with a series and particularly the application of the ratio test to the given series.

The ratio test requires us to find the limit of an+1/an as n approaches infinity. To find this ratio, we consider an+1 by replacing n with n+1 in the expression for an. Calculations for the ratio involve factorial manipulation and power operations.

The series in question is ∑ n=1[infinity](3n)!/28ⁿ (n!)^3 and we define an element of the series as an = (3n)!/28ⁿ (n!)^3.