1/10²+1/11²
a=1/10*11+1/11*12+1/12*13+---+1/1000*1001=
=(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+--+(1/1000-1/1001)=
=1/10-1/1001
b=1/9*10*11+1/10*11*12+---+1/999*1000*1001=
=(1/2)[(1/9*10-1/10*11)+(1/10*11-1/11*12)+--+
+(1/999*1000-1/1000*1001)=
=(1/2)[1/9*10-1/1000*1001}=0。 005555056
1/10^2+1/11^2+---+1/1000^2和...全部
a=1/10*11+1/11*12+1/12*13+---+1/1000*1001=
=(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+--+(1/1000-1/1001)=
=1/10-1/1001
b=1/9*10*11+1/10*11*12+---+1/999*1000*1001=
=(1/2)[(1/9*10-1/10*11)+(1/10*11-1/11*12)+--+
+(1/999*1000-1/1000*1001)=
=(1/2)[1/9*10-1/1000*1001}=0。
005555056
1/10^2+1/11^2+---+1/1000^2和近似值a的误差小于0。006,
其中a=1/10-1/1001。
。收起
