(1-2的2次方分之1)(1-3的2次方分之1)(1-4的二次方分之1)*······(1-100的二次方分之一)
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(1-2的2次方分之1)(1-3的2次方分之1)(1-4的二次方分之1)*······(1-100的二次方分之一)
=(1-1/(2^2))(1-1/(3^2))......(1-1/(100)^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).....(1-1/100)(1+1/100)
=1/2 *3/2*2/3*4/3*3/4*5/4.........................99/100*101/100
=1/2*101/100=101/200
=(1-1/(2^2))(1-1/(3^2))......(1-1/(100)^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).....(1-1/100)(1+1/100)
=1/2 *3/2*2/3*4/3*3/4*5/4.........................99/100*101/100
=1/2*101/100=101/200
展开全部
(1-2的2次方分之1)(1-3的2次方分之1)(1-4的二次方分之1)*······(1-100的二次方分之一)
=(1-1/(2^2))(1-1/(3^2))......(1-1/(100)^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).....(1-1/100)(1+1/100)
=1/2 *3/2*2/3*4/3*3/4*5/4.........................99/100*101/100
=1/2*101/100=101/200
=(1-1/(2^2))(1-1/(3^2))......(1-1/(100)^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).....(1-1/100)(1+1/100)
=1/2 *3/2*2/3*4/3*3/4*5/4.........................99/100*101/100
=1/2*101/100=101/200
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