`(x)/(1.2)+(x^(2))/(2.3)+(x^(3))/(3.4)+....=`

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The series expansion of log_(e) [(1 + x^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

If f(x)=(x^(2))/(1.2)-(x^(3))/(2.3)+(x^(4))/(3.4)-(x^(5))/(4.5)+..oo then

If f(x)=(x^(2))/(1.2)-(x^(3))/(2.3)+(x^(4))/(3.4)-(x^(5))/(4.5)+..oo then

If |x|lt1 then (1)/(2)x^(2)+(2)/(3)x^(3)+(3)/(4)x^(4)+....=

If x ne 0 then the sum of the series 1+(x)/(2!)+(2x^(2))/(3!)+(3x^(3))/(4!)+..to infty is

If x ne 0 then the sum of the series 1+(x)/(2!)+(2x^(2))/(3!)+(3x^(3))/(4!)+..to infty is

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...