(1+2/3)*(1-2/3)*(1+2/5)*(1-2/5)······*(1+2/99)*(1-2/99)怎么算

(1+2/3)*(1-2/3)*(1+2/5)*(1-2/5)······*(1+2/99)*(1-2/99)怎么算
(1+2/3)*(1-2/3)*(1+2/5)*(1-2/5)······*(1+2/99)*(1-2/99)怎么算

(1+2/3)*(1-2/3)*(1+2/5)*(1-2/5)······*(1+2/99)*(1-2/99)怎么算
=[1-(2/3)^2]*[1-(2/5)^2]*[1-(2/7)^2].*[1-(2/99)^2]
(3^2-2^2) * (5^2-2^2) * (7^2-2^2). * (99^2-2^2)
=------------------------------------------------------------------------------
3^2 * 5^2 * 7^2 . * 99^2
(3+2)(3-2)(5+2)(5-2)(7+2)(7-2).(99+2)(99-2)
=--------------------------------------------------------------------------------
3*3*5*5*7*7*9*9*.*99*99
分子的加法和减法分开算
(5*7*9*11*.*97*99*101)(1*3*5*7*9.*97)
=-----------------------------------------------------------------------------------
3*3*5*5*7*7*9*9*.*99*99
这下看出来了吧?
=（1*3*99*101）/（3*3*99*99）=101/297