Question

(1-2的2次幂分之1)×(1-3的2次幂分之1)×(1-4的2次幂分之1)×.×(1-99的2次幂

Answer 1

用平方差

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/99)(1+1/99)

=(1/2)(3/2)(2/3)(4/3)……(98/99)(100/99)

中间约分

=(1/2)(100/99)

=50/99