#1 Determine the convergence or divergence of the following *sequences* be sure to tell me exactly which test you are using - also write some words about it. lim a) 10 points b) 10 points n { 1024+(100)n n } lim { n+24 n+1 } n Beware: - is indeterminate it is *not* zero c) 10 points n ( 2+2 n) (8 n2+ 24) lim n ------ End of SEQUENCES start SERIES -----#2 Represent the repeating decimal as a sum using sigma notation. 0.237123712371 ... a) 5 points b) 5 points 309.309309309 ... #3 Rewrite the following series using sigma notation: a) 10 points: 5 25 125 1+ + + +... 7 49 343 b) 10 points: what is the as n Show all work !! #4 Determine convergence or divergence by the method or test indicated. Alternate methods or tests are not acceptable. a) 15 points 4n 2 3 /2 45 Integral Test show your triangle and labeled it n=3 properly Hint: x = 2sec() b) 15 points n=3 ( 3 n1 ) ! n2 Ratio Test Hint: (3n+2)! = (3n+2)(3n+1)(3n)(3n-1)! c) 15 points n=1 ln (n) n2 2 Limit Comparison Test hint: bn = 10/ n hint: ln(n) < n for n 1