Use differentiation to find a power series representation for the function. Make sure the first term in your series is not 0.\ $f(x) = frac{x}{(1 + 3x)^2}$ \ $sum_{n=0}^{infty} ( ext{ })$
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However, if we want to find a general formula for the coefficients, we can differentiate the function: f'(x) = 6 + 18x And again: f''(x) = 18 Now, we can use the formula for the nth term of a power series: a_n = f^n(0) / n! For n = 0, we have: a_0 = f(0) = Show more…
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