Question

一些简算题一、1乘2+2乘3+3乘4+4乘5+5乘6+...+29乘30二、1 1 1 1_______ +______

Answer 1

S1=1*2+2*3+.+29*30

S2=1*1+2*2+.+29*29

S1-S2=1+2+.+29=29*30/2=435

S2=29*30*59/6=8555.

所以S1=8555+435=8990

S=(1/1-1/2)-1/2*(1/1-1/3)

+(1/2-1/3)-1/2*(1/2-1/4)

+(1/3-1/4)-1/2*(1/3-1/5)

+…………

+(1/19-1/20)-1/2*(1/19-1/21)

+(1/20-1/21)-1/2*(1/20-1/22)

=(1-1/21)-1/2*(1+1/2-1/21-1/22)

自己化简一下