(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)

(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)
(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)

(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)
分子
=（1+1/2+1/3+1/4+……+1/99+1/100）-2*（1/2+1/4+……+1/100）
=1+1/2+1/3+..+1/100-(1/1+1/2+1/3+...+1/50)
=1/51+1/52+…+1/99+1/100
分母
=1/(100-1)(101+1)+1/(102-2)(102+2)+...+1/(150-50)(150+50)
=1/100(1/102+1/104+...+1/200)
=1/200(1/51+1/52+...+1/100)
所以,
原式=(1/51+1/52+…+1/99+1/100)/[1/200(1/51+1/52+...+1/100)]
=1/(1/200)
=200