For n 0, 1, ..., 20, we compute the quantities Using integration by parts, we obtain the following recurrence: Ko-e-1 wheree 2.71828182845905 is the base of the natural algorithm. A computation on a machine with approximately 16 decimal digits of accuracy gives the following results: 0.718281828459045 0.563436343081910 0.170519064953013 15 0.160495854163853 16 0.150348161837404 0.162363077223183 18 0.204253561558257 19 6.599099498065924 20 -129.263708132859420 17 (a) Are the computed numbers "correct"? (b) What is happening to the round-off error in this recurrence? Provide an anal- ysis. (c) Describe an algorithm which will find Ki, K2o accurately, and explain why your new algorithm is expected to work well For n 0, 1, ..., 20, we compute the quantities Using integration by parts, we obtain the following recurrence: Ko-e-1 wheree 2.71828182845905 is the base of the natural algorithm. A computation on a machine with approximately 16 decimal digits of accuracy gives the following results: 0.718281828459045 0.563436343081910 0.170519064953013 15 0.160495854163853 16 0.150348161837404 0.162363077223183 18 0.204253561558257 19 6.599099498065924 20 -129.263708132859420 17 (a) Are the computed numbers "correct"? (b) What is happening to the round-off error in this recurrence? Provide an anal- ysis. (c) Describe an algorithm which will find Ki, K2o accurately, and explain why your new algorithm is expected to work well