I want a hand written thoroughly solved explained

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, ...} (d) ( 4, 8, 16, 32, ...} 2. Determine whether the sequence converges or diverges. If it converges, find the limit. (a) an = 5Vn + 2. (b) an = (-1)n (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+4) 1/2 1-+00 - cos(1) (c) lim n2 (1 - cos(1) - el - 1 2 n2 + 1 \\ [ (n+ 1 ) - 2 (d) lim 2n2 + 3 (e lim In(n +2) \\ nlon 1-+00 In n 4. Prove the following limits, using the limit definition: lim 2n + 5 1-+00 5n - 3n - 7 3 (b) lim n-+0 502 - 2 5. Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (a) -4+16 - 8+... (b) 10 - 2+0.4 -0.08 + ... (c) Zin=1 12(0.73) -1 (d) 50 (-3)n-1 4n (e) Soo 3n+1 Ln=0 (-2" )