[Calculus] the function f ( x ) = 3 x ln ( 1 + x ) is represented as a power series

Question

The function  is represented as a power series f(x)= ∑∞_n=0 c_nxⁿ

Find the specified coefficients in the power series.

C₂₌

C₃₌

C₄₌

C₅₌

C₆₌

Find the radius of convergence  of the series.

Answer 1

The Taylor series for ln(1+x) =∑x^k(-1)^k+1/k where k runs from 1 to ∞.

You do the multiplication by 3x to get your answer.

P.S. If you don't know how to get the power series, here is a hint:

ln(1+x) = ∫dx/(1+x).