The function f(x)=10xln⁡(1+x)\displaystyle {f{{\left({x}\right)}}}={10}{x}{\ln{{\left({1}+{x}\right)}}} is represented as a power series
f(x)=∑n=0∞cnxn.\displaystyle {f{{\left({x}\right)}}}={\sum_{{{n}={0}}}^{\infty}}{c}_{{n}}{x}^{{n}}.

Find the specified coefficients in the power series.
c2=\displaystyle {c}_{{2}}=  
c3=\displaystyle {c}_{{3}}=  
c4=\displaystyle {c}_{{4}}=  
c5=\displaystyle {c}_{{5}}=  
c6=\displaystyle {c}_{{6}}=  

Find the radius of convergence R\displaystyle {R} of the series.
R=\displaystyle {R}=   .

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