3. Let (S1) represent the series n + 5 n! n=in3 + n +3 and ($2) represent the series M n=inn Which one of the assertions below is true ? (A) Both series are convergent. (B) Both series are divergent. (C) (S1) is convergent and ($2) is divergent. (D) (S1) is divergent and ($2) is convergent. (E) None of (A) - (D). 4. The exact value of 1 3 x(x - 1)2 dx is (A) In ( ) + - 3 (B) In 3 (C) In CO IC (D) In + 3 (E) In (5 + 1 3 (F) In - Co /H (G) None of (A) - (F). 5. The exact value of the series _ (3)" + 2(n/2) (-1)n + n! (2n + 1)!] is (A) ev2 + sin(1) + 2 (B) e2 + cos(1) + 1 (C) ev2 + sin(1) - 2 (D) ev2 + cos(1) + 1 (E) e2 - sin(1) + 1 (F) ev2 + sin(1) + 1 (G) None of (A) - (F). 6. A sequence (an) is defined recursively by a1 = 3 and anti = V21 + 4an for all natural numbers n. Which one of the following assertions is true about the sequence (an) ? (A) It is increasing and converges to 7. (B) It is decreasing and converges to 5. (C) It is increasing and converges to 5. (D) It is decreasing and converges to 7. (E) It diverges. (F) None of (A) - (E)