-(1/2),-(1/6),-(1/12),-(1/20),-(1/30),-(1/42),-(1/56),-(1/72),-(1/90),-(1/10)
这10个负数的和是多少?不要过程,只要答案..
參考答案:因为:
1/2=1/(1*2)=1-(1/2);
1/6=1/(2*3)=(1/2)-(1/3);
1/12=1/(3*4)=(1/3)-(1/4);
……
1/90=1/(9*10)=(1/9)-(1/10).
所以原式可转化为:
-[(1/2)+(1/6)+(1/12)+……+(1/90)+(1/10)]
=-[1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+……+(1/9)-(1/10)+(1/10)]
=-[1-(1/10)+(1/10)]
=-1