Question

[1-(1/11)^2]*[1-(1/12)^2]*……[1-(1/99)^2]

Answer 1

用平方差

原式=(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)(12/13)(14/13)……(98/99)(100/99)

=(10/11)(100/99)

=1000/1089