Question #61a81

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Answer 1 · 2017-08-01T19:10:53

The series is #=sum_(n=1)^oo(-1)^(n+1)x^(3n)/n#

The Maclaurin series of a function #f(x)# is a Taylor series of the function #f(x)# at #a=0#

#f(x)=f(0)+(f'(0))/(1!)x+(f''(0))/(2!)x^2+(f'''(0))/(3!)x^3+..........#

The Series for #ln(1+x)# with center at #0# is

#=x-x^2/2+x^3/3-x^4/4+..............#

#=sum_(n=1)^oo(-1)^(n+1)x^n/n#

The Series for #ln(1+x^3)# with center at #0# is obtained by replacing #x# by #x^3#

#=x^3-x^6/2+x^9/9-x^12/4+..............#

#=sum_(n=1)^oo(-1)^(n+1)x^(3n)/n#