Unformatted text preview: n + 1 Â¶ n = Â± n n + 1 Â¶ n < 1 . (Again it is possible to compute the limit; see exercise 2 .) Exercises 1. Compute lim x â†’âˆž x 1 /x . â‡’ 2. Use the squeeze theorem to show that lim n â†’âˆž n ! n n = 0. 3. Determine whether { âˆš n + 47âˆš n } âˆž n =0 converges or diverges. If it converges, compute the limit. â‡’ 4. Determine whether n 2 + 1 ( n + 1) 2 ï¬€ âˆž n =0 converges or diverges. If it converges, compute the limit. â‡’ 5. Determine whether n + 47 âˆš n 2 + 3 n ï¬€ âˆž n =1 converges or diverges. If it converges, compute the limit. â‡’ 6. Determine whether 2 n n ! ï¬€ âˆž n =0 converges or diverges. â‡’ 10.2 Series While much more can be said about sequences, we now turn to our principal interest, series. Recall that a series, roughly speaking, is the sum of a sequence: if { a n  n âˆˆ Z â‰¥ }...
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 Fall '07
 JonathanRogawski
 Math, Calculus, Derivative, Sequences And Series, Mathematical analysis, n1/n } converges

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