solve the following questions ( handwritten solution only neatly and clean box final answer) thankyou!

Topics: Sequences and Series Multiple Choice. Choose the letter that corresponds to your answer. In a particular item, if the answer is not among the choices or there are more than one of the choices that correctly answer that question, choose E. In some items (with blanks), you will have to provide the values(s), word(s) or expression(s) that will make the given statement true. Input your answers on the MS Forms provided. 1. Given the sequence 1 1 1 1 1 4' 10'28 82 244' ,... which of the following formula represents the general term of the said sequence, starting with n = 1? (A) (B) 372-1 (C) 3n+1 (D) 3n - 2. Determine which of the following represent the first four terms of the sequence {tanna },. (A) 0, 1, -1, 1 (C) -1,1, -1,1 (B) 1,0, -1,0 (D) 1, -1, 1, -1 3. Let (-1 )" 78 4 1 ) 73 nel If an = (-1)" 3 4 1, then a3- (A) = 14 (B) = 27 27 (D) is undefined 27 14 (C) = 14 4. Which of the following is true? (A) 3 (-1) _13 converges to 0. converges to 2. n=1 In=1 (B) (-1) " n's converges to 2. (D) (1 is divergent. 5. Consider sequences {an} and {b,}, where an - co as n -+ co and by = (-1)". Which of the following is divergent? (A) {30, - 1} (B) {(b,)2 } (C) ((an )? + 3) (D) 1 1000 3 6. Which of the following sequences converge to (? (A) (2) =1 (B) {1+ (-1)")=1 7. Which of the following sequences does not converge to 0? (A) {nzen), (B)8. Which of the following is true about the sequence onsin "} ? (A) It converges to 1. (C) It converges to 0 (B) It converges to ? (D) It is divergent. 9. Which of the following statements is true? (A) Insin _ is strictly deccreasing. (C) {1+ (-1)"), is strictly increasing. (B) {nze "joe "In=1 is strictly increasing. (D) { is strictly decreasing . For the next 3 items, choose A if the statement is True and B if the statement is False. fun+ > 1 for all n 2 1, then the sequence {an} is strictly increasing. an 11. The sequence {tan 'n}, is neither decreasing nor increasing. 12. An increasing sequence is bounded above by its first term. 13. Let . If {S,} is the sequence of the partial sum of this series, then S4 = (A) 0 62 (B) 125 (C) 25 (D) 62 25 14. Which of the following series is convergent? (A) So (B) En (D) (n - 5) n= 1 n= 1 For the next 6 items, choose A if the statement is True and B if the statement is False. 15. The series 2 -n is convergent and the common ratio r = 3" 16. The series _ is convergent and its common ratio is , n=1 17. The series _ ( _ 3) "-1 is convergent and has a sum of = 18 18. The series 2 n has a sum of n= 1 19. The series _ (n + 37 ) is divergent. n=1 20. The series is convergent. n(n + 1)