Find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = 5(1 − x)−2 f(x) = ∞ n = 0 find the associated radius of convergence r. r =

We can use the fact that, for ,

Notice that

so that

By the ratio test, this series converges if

so the series has radius of convergence .

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.