A function f is defined by f(2) =++ . 3 4 n+1 8. n+1 ... + 34 3n+1 3n+1 for all a in the interval of convergence for the power series. (a) Find the radius of convergence for the power series. (b) Find the interval of convergence for the power series. (c) Find the power series representation for f'(x) and state its radius of convergence. (d) Find the power series representation for | f(r)dr.

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Q: find a power series for the function and the intervals of convergence  f(x)=2x/1-x2

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A: Given:

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A: Solution is given below:

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A: ∑k=1∞ 3x+5k2k

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Q: find the interval of convergence of the power series

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