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Calculus  II                                           Quiz #8                     April 23, 2003

Name_________________            R.  Hammack                  Score ______
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(1) Decide if the following sequences converge or diverge. In the case of convergence, state the limit.

(a)   { 4sec(5/n)   } _ (n = 1)^∞



(b)    {(n + ln(n))/(3n + 1)} _ (n = 1)^∞




(c)    {(-1)^n/( n^2 ) + 1/n !} _ (n = 1)^∞



(2)   Consider the sequence defined recursively as a_1 = 1,   and   a_ (n + 1) = a_n/(1 + a_n).

(a) Explain why this series converges.

 


(b)  Find the limit.