Please show all steps clearly, thank you.

1. Test the series for convergence or divergence : ( - 1 )n n - 1 n=2 2. Determine if the series converges conditionally or absolutely or diverges : 00 ( - 1 )n ( 12 ) 3 n = 1 3. Find the interval of convergence of the power series using the ratio test: 00 [(-1)n (x - 2 ) n n n=1 4. Approximate In 1. 1 using the Taylor polynomial of degree 3 for the function f(x) = In x with center at a = 1. 5. Find the first four terms of the Taylor series for the function f(x) = cos (4x) with center at a = 1/3. Write the coefficients in simplest exact form