Evaluate the indefinite integral as a power series f(x) = 1 tan-1(x7) dx n=0 What is the radius of convergence R? R= -/0.77 points
Evaluate the indefinite integral as a power series x7 In(1 x) dx f(x) = C + n=0
What is the radius of convergence R?

A.

For convergence  since |x| > 1

The radius of convergence R = 1

B.

For convergence  since |x| < 1

The radius of convergence R = 1

Step-by-step explanation:

A.

Given that:

Let recall that for Power series of tan⁻¹ (x)

Then

Thus;

For convergence  since |x| > 1

The radius of convergence R = 1

B.

Recall that for power series of,

Thus;

For convergence  since |x| < 1

The radius of convergence R = 1

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: