Problems 1. Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (a) {1,1,1,1,...} (b) {1, 0, 1, 0, 1, 0, 1, ...} (c) {5, 8, 11, 14, 17, ...} 3 9 27 ...} (d) {16' 32. 2. Determine whether the sequence converges or diverges. If it converges, find the limit. (a) an=5n +2. (b) an = (-1) n (c) an = 2n cos(n2) 2n 2n (d) an = en+2 3. Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded? (a) an = = cos(n) (b) an = 2n+3 (c) an = n(-1)n (d) an = 2 + (-1)" 4. Prove the following limits, using the limit definition: 2n +5 (a) lim no n 2 3n-7 = 2 5' 3 (b) lim nx 5n 2 5 5. Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (a) -4+16-64+ 3 9 (b) 102+0.4 0.08 + ... (c) 1 12(0.73)n-1 (d) n=1 (-3)n-1 (e) 500 4n 3n+1 n=0 (-2) 6. Express the number in canonical rational form. (a) 0.8 (b) 0.46 (c) 0.1234567