Question: Suppose a function f is defined by setting f(x) 32n+1x5n+7 (that is, f is defined to be the limit of the n=0 series, and

Suppose a function f is defined by setting f(x) 32n+1x5n+7 (that is, f is defined to be the limit of the n=0 series, and the domain of f is the set of real numbers for which the series converges). 1. The power series 32+1x5n+7 is a geometric series. Using this information: identify for which values n=0 of x the series converges, and find a formula for f(x) which is not expressed as a series. 2. Consider the statement: (1) = -32 31 Explain what is wrong with the statement. [2 marks] [1 marks] 3. Give a series which is equal to f'(x) on some interval. What is the radius of convergence of this series? [2 marks]

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