Could someone please check my work

. Prove that s, & monotones 8. " 2 and Sa. ) - \\ 25. + I for all n E N * = 2 "3 -/2(2) + 1 = V3 = 2.236067977 *3 =/2(v3) + 1 = 2.339259702 84 = 2(2.339259702) + 1 = 2.382964415 2(2.382964415) + 1 = 2.401234855 2(2.401234855) + 1 = 2.408831607 2(2.408831607) +1 = 2.411983253 2(2.411983253) +1 = 2.413289561 59 = 2(2.413289561) + 1 = 2.413830798 The sequence, (Sn), seems to be increasing and bounded by [2, 2.42]. To prove (8n) is increasing and thus monotone by definition 4.3.1, apply induction: Base step: For n = 1 , $1 = 2 and $2 = 2.236067977 = $1