Please help with the following questions:

The Ratio Test. CK) Suppose that Z on is a series with positive terms, and lim on" = L (L could be 00). ":1 "Ir>00 an :0 o If L 1 then the series 2 an is divergent. n=1 Remarks. . an+1 . . . . . . o If hm = l, the Ratlo test in inconclusive, that is, no concluslon can be drawn about the convergence of the nroc an 0C series E on. n=1 0 The Ratio test is usually conclusive if the nu' term of the series contains an exponential or a factorial. DC: 211 1. EH n:1 371 2. Elm eon" 3.:a 11:1 The Root Test. 30 Suppose that E on is a series with positive terms, and lim ("/E." = L {L could be cc). 'HPCO n=1 DD 0 If L 1 then the series > an is divergent. n=1 Remarks. . If lim Van = 1, the Root test in inconclusive, that is, no conclusion can be drawn about the convergence of the n-+0o series > an. n=1 . The Root test is convenient to apply if the nth term of the series contains an nth power. 1. E ( 2n + 3 ) n=1 3n + 2) 2. 3. (AP.) You can use any convergence test. 9. Which of the following series converge? II. n! III. S n+1 (n)(n + 2) (n +3) (A) I only (B) II only (C) III only (D) I and III only (E) I, II, and