Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 + 1 f(x) = sigma^infinity_n = 0 (-1)^n x^2n+1 6^n Determine the interval of convergence. (Enter your answer using interval notation.)

Looks like your function is

Rewrite it as

Recall that for , we have

If we replace with , we get

By the ratio test, the series converges if

Solving for gives the interval of convergence,

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

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step-by-step explanation:

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