①x-1分之1减x+1分之1减x的二次方+1分之一减x的四次方+1分之4

1/（x-1）-1/(x+1)-2/(x^2+1)-4/(x^4+1)
=2/(x^2-1)-2/(x^2+1)-4(x^4+1)
=4/(x^4-1)-4/(x^4+1)
=8/(x^8-1)
2/(x+1)(x+3)=[(x+3)-(x+1)]/(x+1)(x+3)=1/(x+1)-1/(x+3)
所以原式=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5).+1/(x+2007)-1/(x+2009)
=1/(x+1)-1/(x+2009)
a2=1-1/x=(x-1)/x
a3=1-x/(x-1)=-1/(x-1)
a4=1-(x-1)/(-1)=1+x-1=x
a5=a2=(x-1)/x
以3为周期a2000=a2=(x-1)/x

x-1分之1可以这样录入：1/(x-1)
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(1)1/(x-1)-1/(x+1)-2/(x^2+1)-4/(x^4+1)
=[(x+1)-(x-1)]/(x^2-1)-2/(x^2+1)-4/(x^4+1)
=2/(x^2-1)-2/(x^2+1)-4/(x^4+1)
=4/(x^4-1))-4/(x^4+1)
=8/(x^8-1)