I want it solved and well explained for understanding

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, ...} (d) (4, 3, 16, 32, . . . } 2. Determine whether the sequence converges or diverges. If it converges, find the limit. (a) an = 5vn + 2. (b) an = (1)n 2vn (c) an = cos(n?) (d) an = entz 3. Using equivalent infinitesimals or equivalent growth, find the following limits: (a) lim n-21 -cos(1) el - 1 (b) lim ((1+1)1/2 - cos(1) ) (c) lim n2 (1- cos(1) _ n2 + 1 \\ In ( n+ 1 ) - 2 (d) lim 2n2+3 In(n + 2) \ lan (e lim n-+00 Inn 4. Prove the following limits, using the limit definition: (a lim 2n + 5 n-+00 5n - 2 3n 3 (b) lim n-+0 5n - 2 5. Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (a) -4+ 16 - 64 + ... (b) 10 - 2 +0.4 - 0.08 + ... n=1 12(0.73) 7-1 (d) too (-3 )n -1 47 3n+ 1 (e) En-o (= 2")