计算1-1⼀2+1⼀3-1⼀4+···+1⼀99-1⼀100的结果

有什麽方法呢???有更简单的方法吗?
2025-03-15 15:29:17
推荐回答(4个)
回答1:

一种做法就是上面的办法
另一种做法是
1-1/2+1/3-1/4+···+1/99-1/100
=1+1/2+1/3+1/4+···+1/99+1/100-2(1/2+1/4+···+1/100)
=1+1/2+1/3+1/4+···+1/99+1/100-(1+1/2+···+1/50)
=1/51+1/52+···+1/100
只能化成这样了,剩下来的只能硬来,你学过数学分析就知道了

回答2:

解:1-1/2=1×1/2,
1/3-1/4=4/12-3/12=(1/3)(1/4),
1/5-1/6=6/30-5/30=(1/5)(1/6),
…… ……
也就是说原式=1×(1/2)+(1/3)(1/4)+(1/5)(1/6)……+(1/99)(1/100)>1/2

再有,根据上述原理,原式还可以写作:1-(1/2)(1/3)-(1/4)(1/5)-(1/6)(1/7)……-(1/98)(1/99)-1/100<1。

回答3:

原式=1/(1*2)+1/(3*4)+···+1/(99*100)=

回答4:

DIM i;
DIM count=0;
For i=1 To 100{
count=count+(1/i)*[(-1)^i];
Next i;
}

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