(1-1/100)(1-1/99)(1-1/98)…(1-1/4)(1-1/3)(1-1/2)请大家帮忙,
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![(1-1/100)(1-1/99)(1-1/98)…(1-1/4)(1-1/3)(1-1/2)请大家帮忙,](/uploads/image/z/6854893-61-3.jpg?t=%281-1%2F100%29%281-1%2F99%29%281-1%2F98%29%E2%80%A6%281-1%2F4%29%281-1%2F3%29%281-1%2F2%29%E8%AF%B7%E5%A4%A7%E5%AE%B6%E5%B8%AE%E5%BF%99%2C)
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(1-1/100)(1-1/99)(1-1/98)…(1-1/4)(1-1/3)(1-1/2)请大家帮忙,
(1-1/100)(1-1/99)(1-1/98)…(1-1/4)(1-1/3)(1-1/2)请大家帮忙,
(1-1/100)(1-1/99)(1-1/98)…(1-1/4)(1-1/3)(1-1/2)请大家帮忙,
你观察会发现
1-1/100=99/100
1-1/99=98/99
1-1/98=97/98
如果他们相乘
分子分母刚好可以抵消
所以上式=(99/100)*(98/99)*(97/98)*.*(3/4)(2/3)(1/2)
=1/100
100*99+99*1
100×99+100×1
100+99+98+.+1?
1+2+.+99+100
99+1+100?
(100+99*1)+(99+99*2)+(98+99*3)+...+(2+99*99)+(1+99*100)
100+100-99-2+1
100*(100-1)*99
|1/100-1/99|+|1/101-1/100|-|1/100-1/99|=?
计算|1/2-1|+|1/3-1/2|+.+|1/99-1/98|+|1/100-1/99|
求和:|1/2-1|+|1/3-1/2|+.+|1/99-1/98|+|1/100-1/99|
|1/2-1|+|1/3-1/2|+.+|1/99-1/98|+|1/100-1/99|
(1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于?
(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/99)*(1-1/100)=
计算:|100/1-99/1|+|101/1-100/1|-|101/1-99/1|
|1/100-1/99|+|1/101-1/100|-|1/101-1/99|
|1/101-1/99|-|1/100-1/99|-|1/100-1/101|=_____
|1/101-1/99|-|1/100-1/99|-|1/100-1/101|等于多少?