Question

第二小题，急急急啊！

Answer 1

后面一半
a^2+1=a^2-1+2,
2/(a^2-1)=1/(a-1) - 1/(a+1),
(a^2+1)/(a^2-1) = 1 + 1/(a-1) - 1/(a+1),

原式=10-(9+1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11)
=1-(1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11)
=-(-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11)
= - (1/2-1/10-1/11)
=-34/110=-17/55

Answer 2

=10-{[1+2/(2^2-1)]+[1+2/(3^2-1)]+……+[1+2/(10^2-1)]}
=1-[2/(2^2-1)+2/(3^2-1)……+2/(10^2-1)]
=1-{[1/(2-1)-1/(2+1)]+[1/(3-1)-1/(3+1)]+……+[1/(10-1)-1/(10+1)]}
=1-(1-1/3+1/2-1/4+1/4-1/5+……+1/9-1/11)
=1-[(1+1/2+1/3+……+1/9)-(1/3+1/4+……1/11)
=1-(1+1/2-1/10-1/11)
=1/10+1/11-1/2
=-17/55

Answer 3

第一小问，(n^2+1)/(n^2-1)=(n^2-1+2)/(n^2-1)=1+2/(n^2-1)=1+1/(n-1)-1/(n+1)
那么第二小问=10-（1+1-1/3+1+1/2-1/4+1+1/3-1/5+1+1/4-1/6...+1+1/8-1/10+1+1/9-1/11)
=10-[10+(1/2-1/3+1/3-1/4+1/4-....-1/9+1/9-1/10-1/11)]
=-(1/2-1/10-1/11)=-17/55

Answer 4