(1+1/2)x(1-1/2)x(1+1/3)x...x(1+1/99)x(1-1/99)=?
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(1+1/2)x(1-1/2)x(1+1/3)x...x(1+1/99)x(1-1/99)=?(1+1/2)x(1-1/2)x(1+1/3)x...x(1+1/99)x(1-1/99)=?(1+1/2
(1+1/2)x(1-1/2)x(1+1/3)x...x(1+1/99)x(1-1/99)=?
(1+1/2)x(1-1/2)x(1+1/3)x...x(1+1/99)x(1-1/99)=?
(1+1/2)x(1-1/2)x(1+1/3)x...x(1+1/99)x(1-1/99)=?
(1-1/2)x(1+1/2)x(1-1/3)x(1+1/3)x.x(1-1/99)x(1+1/99)
=1/2x3/2x2/3x3/4x4/3x.x98/99x100/99
=1/2x1x1x.x1x100/99
=50/99
整理会发现
原式=1/2 * 2/3 * 3/4 * ...* 99/98 * 98/99 * 100/99
消吧消吧
最后就剩1* 100/99了
结果=100/99
(1/2)*(100/99)=50/99
原式子=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/99)*(1+1/99)
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