For 1-3: show work on this page: 1. Determine whether the following sequence converges or diverges and show/explain why. 2" a,, = (-1)" (-) 2. Find the sum of the infinite geometric series without a calculator: [s( )" n=0 3. Determine whether the series converges or diverges. If it converges, classify the series as absolutely convergent or conditionally convergent. (see notes/thm to interpret this/apply thm) (-1)" (1) n= 1 n'For 1-3: show work on this page: 1. Determine whether the following sequence converges or diverges and show/explain why. 2" a,, = (-1)" (-) 2. Find the sum of the infinite geometric series without a calculator: [s( )" n=0 3. Determine whether the series converges or diverges. If it converges, classify the series as absolutely convergent or conditionally convergent. (see notes/thm to interpret this/apply thm) (-1)" (1) n= 1 n'4. Choose 4 of the following. Determine whether they are convergent or divergent. Be sure to state the rule used and use a different rule per series you choose. (so don't use the same rule/technique for all problems) 5 a ) e) In(2)" 71=1 3n(2n + 7) 14n' +1 b) Son - 3n f) n -10 n=1 7n -2n 14n +n' c) _ 2" 71 -0 9) 2 Vn In' + 1 d) n! h) EC 8 -8 2n!+ 1 + n+l n+2 5. Given the function, f(x) = f(x) = 2+ x a) Write a power series for f(x). b) Write a series expansion of the first four terms and the general term. c) Determine the interval, center and radius of convergence.4. Choose 4 of the following. Determine whether they are convergent or divergent. Be sure to state the rule used and use a different rule per series you choose. (so don't use the same rule/technique for all problems) 5 a ) e) In(2)" 71=1 3n(2n + 7) 14n' +1 b) Son - 3n f) n -10 n=1 7n -2n 14n +n' c) _ 2" 71 -0 9) 2 Vn In' + 1 d) n! h) EC 8 -8 2n!+ 1 + n+l n+2 5. Given the function, f(x) = f(x) = 2+ x a) Write a power series for f(x). b) Write a series expansion of the first four terms and the general term. c) Determine the interval, center and radius of convergence