Geometric Series Sequences and L Hopital s Rule from Old Exams

Thomas' Calculus: Early Transcendentals

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Unformatted text preview: Mat104 Geometric Series, Sequences and L'H^pital's Rule from Old Exams o (1) For which values of x does n=0 enx converge? What is the value when it converges? (2) Evaluate n=4 - 2 3 n . (3) Evaluate n=0 2n + 3n+1 + 4n+2 . 5n 2 + (-3)n . 5n 2 + 2n . 4n (4) Find 2 + n=1 (5) Evaluate n=0 (6) Find lim ln(n2 + n) or show that it does not exist. n ln(n2 - n) 3n3 + 1 does not exist: n4 + n2 + n + 8 n + 17 arctan(n) + 2 (8) Find each lim or show that it does not exist. n 1-n (7) Evaluate or show that limn (9) Find lim n 1 1+ n 2n or show that it does not exist. (10) Find the following limits: 1 1+ n 3 n n (a) lim n (b) lim ln(n + 1000) n ln(n2 ) 1 ...
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