The formula for (3^n)/(2^n + 4^n) is an exponential function. It can also be written as (3/2)^n / (1 + (2/4)^n).
The convergence of (3^n)/(2^n + 4^n) can be explained by using the ratio test. As n approaches infinity, the ratio between consecutive terms approaches a finite value, which indicates convergence.
The limit comparison test is used because it allows us to compare the given series to a known series with known convergence properties. This helps us determine the convergence of the given series without having to evaluate its individual terms.
The limit comparison test for (3^n)/(2^n + 4^n) involves taking the limit of the ratio of the given series to a known convergent series. If the limit is a nonzero finite value, then the given series also converges.
To use the limit comparison test for (3^n)/(2^n + 4^n), we first need to choose a known convergent series to compare it to. Then, we take the limit as n approaches infinity of the ratio of the two series. If the limit is a nonzero finite value, then we can conclude that the given series converges. If the limit is zero or infinity, then the convergence of the given series cannot be determined using this test.