I'm struggling in marked question in this exercise. I already have the answer provided by the book but I did not know the process to get that number. Please help me, thank you much!

31. (a) Sn = 1-(1/4)" 3/4 (b) Converges to 4/3. 33. (a) Sn = (2(n+1) \\ 2 2 (b) Diverges 35. (a) Sn = 51-1/20 1 / 2 (b) Converges to 10. 37. (a) Sn = 1-(-1/3)" 4/3 (b) Converges to 3/4. Thus N/W 39. (a) With partial fractions, an = Sn = 3 (2 - H1 (b) Converges to 9/4 (1 1 (0 + 1 ) )In Exercises 31 -46, a series is given. (a) Find a formula for Sn, the nt partial sum of the series. (b) Determine whether the series converges or diverges. If it converges, state what it converges to. 31. An n=0 32. 2 n=1 33. 15 + 23 + 3 3 + 43 + ... 34. [(-1) 'n n=1 35. 2n n=0 36. M en n=1 37. 1 1 1 WIH + H... 27 81 38. 1 M n= n (n + 1) 0O 39. 3 IM n(n + 2)