(3) (2 points) The terms of a series can also be defined recursively. Suppose 1 and...

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(3) (2 points) The terms of a series can also be defined recursively. Suppose 1 and an+1 = 2 n + 7 aj = an for n > 1 2n + 51 Use an appropriate test to determine whether or not the series converges. (4) (2 points) Generalize the result of the previous exercise. Suppose a1 > 0 and an+1 = f(n)an for some function f. Give a condition on f(n) which would guarantee that such a series converges absolutely. (3) (2 points) The terms of a series can also be defined recursively. Suppose 1 and an+1 = 2 n + 7 aj = an for n > 1 2n + 51 Use an appropriate test to determine whether or not the series converges. (4) (2 points) Generalize the result of the previous exercise. Suppose a1 > 0 and an+1 = f(n)an for some function f. Give a condition on f(n) which would guarantee that such a series converges absolutely.

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