Homework 19 – Summing an Infinite Series 1) Compute the partial sums, S2, S4, and S6. a) 11112 23 3 4 b) 111!kkk 2) Find a formula for the general term an of the infinite series. a) 1 5 25 12512 4 8 b) 23 412 3 41213214321 3) Prove that the following series diverge: a) 110 12nnn b) 01231234 4) Prove whether the following geometric series converge or diverge. If the series converges, find its sum. a) 211 1188 b) 3311nn c) 449nn d) 0825nnn e) 320nne 5) Which of the following are not geometric series? a) 0729nnn b) 431nn c) 202nnn d) 5nn 6) Give a counterexample to show that each of the following statements is false. a) If the general term an tends to zero, then 10nna. b) The Nth partial sum of the infinite series defined by na is aN. c) If an tends to zero, then 1nna converges. d) If an tends to L, then 0nna= L. 7) Suppose that 1nnSais an infinite series with partial sum 225NSN. a) What are the values of 101nna and 165nna? b) What is the value of a3? c) Find a general formula for an. d) Find the sum, 1nnSa. 8)
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