1. (1 point) For each of the following sequences, state a for- 4. (1 point) Determine if the following sequence converges mula for the general term a, where n 2 1. or diverges. [E.g. For the sequence {1, 4,9, 16, 25,36, ...}, you would en- ter n' .] 9(2") + 17 an 9(4") 1111 Note: If it converges, enter the limit as your answer. If it 1 7'4'6'8' diverges to co, -co, or neither enter infinity, -infinity, or diver- gent, respectively. 111 1 - 2' 4'8'16 Answer: 5. (1 point) 4n Consider an 2. (1 point) 2n + 1 Determine if the following sequence converges or diverges. Determine if each of the following converges or diverges. an = Note: If it converges, enter the limit (for the sequence) or the sum (for the series). If it diverges, enter divergent. Note: If it converges, enter the limit as your answer. If it diverges to co, -co, or neither enter infinity, -infinity, or diver- (a) The series _ (a,). Answer: gent, respectively. (b) The sequence {a,, }. Answer: Answer: 6. (1 point) 3. (1 point) Determine if the following series converges or diverges. Calculate the first five terms of the following sequence, start- ing with n = 1. Note: If it converges, consider whether it is geometric or tele- scoping and enter its sum. If it diverges, enter divergent. 3+9" a1 = -2; an+1 = -2an + 9 1=1 7. (1 point) Determine if the following series converges or diverges. Note: If it converges, consider whether it is geometric or tele- scoping and enter its sum. If it diverges, enter divergent. 1=1 8. (1 point) Determine if the following series converges or as = diverges. Note: If it converges, consider whether it is geometric or tele- scoping and enter its sum. If it diverges, enter divergent. 12. (1 point) The function f(x) = 2 can be represented as a power(-2 )0-1 12. (1 point) 2 The function f(x) = (1 -5x) can be represented as a power 9. (1 point) Determine if the following series converges or series of the form diverges. Note: If it converges, consider whether it is geometric or tele- scoping and enter its sum. If it diverges, enter divergent. f ( x ) = [ cax" 18 M in(n + 2) (a) Find the following coefficients of the power series. 10. (1 point) For each of the following series, find the values CO= of x for which it converges. (a) 2 G = Answer: |x 02 = (b) [ x5 " 1=1 (b) Find the radius of convergence R of the series. Answer: (x|