Find a power series representation for the function. determine the interval of convergence. (give your power series representation centered at x = 0.) f(x) = 5 2 − x

I'm guessing the function is

whose first few derivatives are

with a general pattern of

Then has power series (centered at 0)

which is a geometric series, converging only for

(this is the interval of convergence)

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If you know that for

then we can derive the same series by manipulating this result:

1010: 3030

is it i think