Given that 111-2 = Σ x" with convergence in (-1, 1), find the power series for x 1 - 7x9 8 WI Σ n=0 n=0 The radius of convergence is

Let 2 C,(x-9)" be a power series with the radius convergence R=0. Then n =0 Select one: a. The series C(x-9)" is convergent at x = - 9 b. None of them The series 2 Cn(x-9)" is convergent at x = 0 n = 0 d. The series 2 c,(x - 9)" is divergent at x = 9 n =0 e. The series C(x-9)" is convergent at X =9 n=0

Find the interval of convergence of the 6k series Lk=1 · 3

The series True O False (-1)^ n Σn=1 is conditionally convergent.

42n (x + 6)" is convergent if The given power series 9n

The divergence test applied to the series 00 4k (7k + 9)* tells us that the series converges.

Let 2 c,(x - 9)" be a power series with the radius n =0 convergence R= 0. Then Select one: а. The series 2 c,(x - 9)" is convergent at n = 0 X = 0 b. None of them С. The series c,(x - 9)" is convergent at n = 0 X = - 9 d. The series E c,(x - 9)" is divergent at n =0 X = 9 е. The series E c,(x – 9)" is convergent at n = 0 X = 9

The function f(x) = (10x^2)/(1 / 2x)^2 is represented as a power series. Find c1, c2, c3, c4, c5 and find the radius of convergence R for the series.

Find the closed-form expression forf(z)=4z^3 +8z^7 +12z^11 +···+4nz^(4n-1) +.... and then find the radius of convergence of this power series. Justify your answer carefully.

Find the power series and the interval of convergence for f(x)=1/(1-2x)