# an+1 n+4 1. Let {an} be a sequence of positive, real numbers such...

## Transcribed Text

an+1 n+4 1. Let {an} be a sequence of positive, real numbers such that = for all values of n. What an 3n+1 is lim an? Explain how you got your answer. n-100 80 3. Compute lim (2003/25)-2+422 x->0 2.4 4. Consider the series 1 + - - + (a) Write the series in summation notation. (b) Determine the interval of convergence and the radius of convergence for the series. 5. Let f be a function that has derivatives of all orders at x = 2. Let Pn (x) denote the nth degree Taylor polynomial for f centered about x = 2. You are given f(2) = 2, f"(2) = - 1, f"((2) = 0 and f(4)(2) = 3. Suppose Pa(4) = -4. Find Pa(x).

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