Please explain each step!

PART I

1. Diverge or converge conditionally or converge absolutely: (-1), In(n-) co In(n3) 1=2 2. Diverge or converge conditionally or converge absolutely: _(-1)" n=2 n In n 3. Diverge or converge conditionally or converge absolutely: _ (-1)" sin -. n=1 n N 4. Find N so that C(-1)" 1 2n + 1 differs from the sum of the series E(-1)n -by less than 1=1 2n + 1 1000 n=1 (-1) "-1 5. Use the Alternating Series Approximation Theorem to find the sum of the series with less n! n=1 than .0001 error. 6. Determine if the series converges absolutely, converges conditionally, or diverges: (a) _(-1)' In(n + 2) n=2 In(2n) (b) _(-1) " 1 n=1 Vn(c) _(-1)" N n=1 N (-1) "-1 7. Use the Alternating Series Approximation Theorem to find N so that gives the sum of the n=1 (-1) "-1 series with less than .000001 error.1. Determine the interval of convergence: (a) n=0 (b) n=1 15n 2. Determine the interval of convergence: 1 + 2n (a) 1 + 3n 1=0 0 1+ 21 (b) _ 1=0 1 + 3n 1 3. Find a power series for f (x) = (1- x)3 Hint: use differentiation. 4. Find a power series for f (x) =; 1 2 + 3x Hint: Use - x = E x" together with a little bit of algebra. 1=0 2 - 3x 5. Find a power series for f (x) = 2x2 - 3x + 1 Hint: First rewrite f(x) using partial fractions. 2n 6. Determine the interval of convergence of 1=0 1 7. Write the function f (x) = 1 _ 312 as a power series and determine the radius of convergence