calculuuuuusssss

Question

The function 𝑓(𝑥)=2𝑥ln(1+𝑥)f(x)=2xln⁡(1+x) is represented as a power series: 

𝑓(𝑥)=∑𝑛=0∞𝑐𝑛𝑥𝑛f(x)=∑n=0∞cnxn

Find the following coefficients in the power series. 

𝑐2=c2=  

𝑐3=c3=  

𝑐4=c4=  

𝑐5=c5=  

𝑐6=c6=  

Find the radius of convergence 𝑅R of the series. 

𝑅=R=   . 

Answer 1

The power series for ln(1+x) = x-(x²/2)+(x³/3)-(x⁴/4)....which converges for x<=1

You should be able to see the answer from that information.