Please help with these Qs ASAP

THANK YOU

# 10: Which of the following Equences converge? . (1)'H1 n2 (1) an = H2 + 3 _1 n+1\" (ii) an = ( Hi 3 (iii) an = sin(mt) (iv) (13le = cosm) (A) (i) and (iv) only (B) all of them. (C) (ii) and (iv) only (D) (i) only (E) (i) and (iii) only (F) (i) only (G) none of them (H) (ii) and (iii) only \f#6: Use the Comparison Theorem to determine which of the following integrals converge. (i) 1 31 air oz: x10_2 (ii) 2 x7 (it 1Tf22eoeit (iii) 0 x3e dx (A) (i) and (ii) only (B) none of them (C) (i) only (D) all of them (E) (i) and (iii) only (F) (ii) and (iii) only (G) (ii) only (H) (iii) only #7: Suppose that a sequence is defined by a1 = 2, an+ 1 = 4-dy. To show that a, is monotonic using mathematical induction, which of the following would be the second step? 1 (A) Assume 4-ax+ 2 =4- ax+ 1 and show that axt 1 = ak (B) Assume ak + 1