Question

1乘1乘3乘4分之1+2乘3乘4乘5分之1+3乘4乘5乘6分之1+…+20乘21乘22乘23分之1

Answer 1

1/(1*1*3*4)+1/(2*3*4*5)+1/(3*4*5*6)+.+1/(20*21*22*23)

=(1/3)*3*(1/(1*1*3*4)+1/(2*3*4*5)+1/(3*4*5*6)+.+1/(20*21*22*23))

=(1/3)*(1/(1*1*3)-1/(1*3*4)+1/(2*3*4)-1/(3*4*5)+1/(3*4*5)-1/(4*5*6)+.+1/(20*21*22)-1/(21*22*23))

=(1/3)*(1/(1*1*3)-1/(1*3*4)+1/(2*3*4)-1/(21*22*23))

然后自己化简就好了

主要是先观察出特点,可以看出每个分母的第一个数与最后一个相差3,所以想到拆项.