1) sin^2 x=(1-cos2x)/2
=1/2-1/2*cos2x
=1/2-1/2*[1-(2x)^2/2!+(2x)^4/4!...+(-1)^n(2x)^2n/2n!+..]
=x^2-2^3x^4/4!..-(-1)^n*2^(2n-1)*x^2n/(2n)!+...
收敛区间为R
2)ln(1+x)=x-x^2/2+x^3/3-....
(1+x)ln(1+x)=[x-x^2/2+x^3/3-x^4/4+.....]+[x^2-x^3/2+x^4/3-...]
=x-x^2(1/2-1)+x^3(1/3-1/2)-x^4(1/4-1/3)+......-(-1)^nx^n(1/n-1/(n+1))+..
收敛区间为(-1, 1]
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