Please help with the following questions:

The Comparison Test. ac 5X3 Suppose that Z a\" and Z 3)" are series with positive terms, and an 3 bn for all n (or for \".0. large). n21 n21 IX; (X) o If E b\" is convergent then E an is also convergent. 11:1 11:1 7X2 30 o If 2 a\" is divergent then 2 b" is also divergent. 11:]. 12:1 00 1 1. E 3.. + 1 \"O 5 2 7; n2 +4n+ 3 m sin?) 2 3- Z( n J :3 | \\ e Inn 4. ET :1 i \\ ,_. The Limit Comparison Test. DC x . . . . . (L . . . Suppose that E on and E bn are series With posmve terms. If 11m bl = c where (3 IS a. brute number and (t > 0. then nDoc 11:1 n=l n. either both series converge or both diverge. 1 1'Z3n_1 \":1 2. 272 + 3 n=1 502 + 1 5 3. n = 2 4n + 3 4. n=2 V3n - 2 5. 2n2 + 3n n=2 Vn5 + 5 6. sin n= 1 7. (AP). 10. Which of the following series converges? (A) M : 3n in + 2 18 (B) S. 3n in2 + 2 (C) (D) (E)