lanedance said:when you sub in for n -> n+1 in exponent of the 4 it should be
[tex] \frac{4^{(2n+1)}}{4^{(2(n+1)+1)}}[/tex]
The Cal 2 ratio test is a method used in calculus to determine the convergence or divergence of an infinite series. It involves comparing the ratio of consecutive terms in the series to a limit, and if that limit is less than 1, the series is said to converge.
To perform the Cal 2 ratio test, you need to first take the limit of the ratio of consecutive terms in the series as n approaches infinity. If this limit is less than 1, then the series converges. If the limit is greater than 1 or does not exist, then the series diverges.
The Cal 2 ratio test is used to determine the convergence or divergence of infinite series. It is a more powerful test than the basic comparison test, as it can determine convergence for certain series that the comparison test cannot.
Mistakes commonly occur when taking the limit of the ratio of consecutive terms, as this can involve complicated algebraic manipulations. It is important to carefully simplify and check your work to avoid errors.
No, the Cal 2 ratio test can only be used for series with positive terms. It also cannot be used for series with alternating signs, such as the alternating harmonic series. In these cases, other tests such as the alternating series test must be used.