(1-2^2/1)x(1-3^2/1)x(1-4^2/1)x...x(1-9^2/1)x(1-10^2/1)的值(算式,
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(1-2^2/1)x(1-3^2/1)x(1-4^2/1)x...x(1-9^2/1)x(1-10^2/1)的值(算式,结果,原因)
![(1-2^2/1)x(1-3^2/1)x(1-4^2/1)x...x(1-9^2/1)x(1-10^2/1)的值(算式,](/uploads/image/z/20124217-1-7.jpg?t=%EF%BC%881-2%5E2%2F1%29x%281-3%5E2%2F1%29x%281-4%5E2%2F1%29x...x%281-9%5E2%2F1%29x%281-10%5E2%2F1%29%E7%9A%84%E5%80%BC%EF%BC%88%E7%AE%97%E5%BC%8F%2C)
(1-2^2/1)x(1-3^2/1)x(1-4^2/1)x...x(1-9^2/1)x(1-10^2/1)
=(1+2/1)(1-2/1)(1+3/1)(1-3/1)(1+4/1)(1-4/1)……(1+9/1)(1-9/1)(1+10/1)(1-10/1)
=(1+2/1)(1+3/1)(1+4/1)……(1+9/1)(1+10/1)*(1-2/1)(1-3/1)(1-4/1)……(1-9/1)(1-10/1)
=2/3*3/4*5/4*……*9/10*10/11*2/1*3/2*4/3*9/8*10/9
=2/11*10/1
=20/11
=(1+2/1)(1-2/1)(1+3/1)(1-3/1)(1+4/1)(1-4/1)……(1+9/1)(1-9/1)(1+10/1)(1-10/1)
=(1+2/1)(1+3/1)(1+4/1)……(1+9/1)(1+10/1)*(1-2/1)(1-3/1)(1-4/1)……(1-9/1)(1-10/1)
=2/3*3/4*5/4*……*9/10*10/11*2/1*3/2*4/3*9/8*10/9
=2/11*10/1
=20/11
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