Please show work!

1. Compute the first five terms of the following sequences (start with n = l}: n! (a) u : 2" lb) bn : it! + [1l'\" (c) en = r: + (r: +1}+{11 + 2} + - - - + {211) {think carefully about this one!) 2. Find a simple formula for the rim term of the following sequences [start with index n = 1]: 1 2 3 (a) 5,5,ZPH Eb) 1r _2r3: _4; 5; _6_. . 1 .. (c) 1,3, ?, 15,31,113. .. 3. Determine the limit for each of the following sequences: H 2112 l 1 (Hint: What tool do you know for showing a function is decreasing?) 4. A sequence is given by the formula an = . Show the sequence is monotone decreasing for :1 3 1. 5. Use L'Hospital's Rule to compute lim :1 1n (1 + %). 31?ch 2\" . List the first five terms of the sequence whose terms are given by the formula on = \"1 for 11 3 1. . . . n + 2 2 7. Determlne the bout of the sequence {an} 2 {}