Question

(1-1/2的2次方)(1-1/3的2次方)(1-1/4的2次方)……(1-1/10的2次方)=?最好有详细过程

Answer 1

(1-1/2的2次方)(1-1/3的2次方)(1-1/4的2次方)……(1-1/10的2次方)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/10)(1+1/10)
=1/2*3/2*2/3*4/3*3/4*5/4*……*9/10*11/10
=1/2*11/10
=11/20

Answer 2

平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)……(9/10)(11/10)
=(1/2)(11/10)
=11/20

Answer 3

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)……(9/10)(11/10)
=(1/2)(11/10)
=11/20