(1-1/121)*(1-1/144)*.(1-9801)=?

原式
=(1-1/11^2)(1-1/12^2)...(1-1/99^2)
=(1-1/11)(1+1/11)(1-1/12)(1+1/12)...(1-1/99)(1+1/99)
=(10/11)(12/11)(11/12)(13/12)...(98/99)(100/99)
=(10/11)(100/99)
=1000/1089