**Unformatted text preview: **n + 1 ¶ n = ± n n + 1 ¶ n < 1 . (Again it is possible to compute the limit; see exercise 2 .) Exercises 1. Compute lim x →∞ x 1 /x . ⇒ 2. Use the squeeze theorem to show that lim n →∞ n ! n n = 0. 3. Determine whether { √ n + 47-√ n } ∞ n =0 converges or diverges. If it converges, compute the limit. ⇒ 4. Determine whether n 2 + 1 ( n + 1) 2 ﬀ ∞ n =0 converges or diverges. If it converges, compute the limit. ⇒ 5. Determine whether n + 47 √ n 2 + 3 n ﬀ ∞ n =1 converges or diverges. If it converges, compute the limit. ⇒ 6. Determine whether 2 n n ! ﬀ ∞ n =0 converges or diverges. ⇒ 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 ∈ Z ≥ }...

View
Full Document

- Fall '07
- JonathanRogawski
- Math, Calculus, Derivative, Sequences And Series, Mathematical analysis, n1/n } converges