-1*(1/2)=-1+(1/2),-(1/2)+(1/3)=-(1/2)+(1/3),-(1/3)*(1/4)=-(1/3)+(1/4),.规律(1)规律:( )用含n的式子表示,n为正整数.(2)运用以上规律计算:(-1*(1/2))+(-(1/2)*(1/3))+(-(1/3)*(1/4))+.+(-(1/2012)*(1/2013))求大神回答啊!
问题描述:
-1*(1/2)=-1+(1/2),-(1/2)+(1/3)=-(1/2)+(1/3),-(1/3)*(1/4)=-(1/3)+(1/4),.规律
(1)规律:( )用含n的式子表示,n为正整数.
(2)运用以上规律计算:(-1*(1/2))+(-(1/2)*(1/3))+(-(1/3)*(1/4))+.+(-(1/2012)*(1/2013))求大神回答啊!
答
-1/n×1/n+1=-1+1/n+1
-1+1/2-1/2+1/3-1/3+1/4-...-1/2012+1/2013
=-1+1/2013
=-2012/2013