计算:1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+33)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/17 08:38:30

计算:1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+33)=?
计算:
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+33)=?

计算:1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+33)=?
原式=1+1/((1+2)*2/2)+1/((1+3)*3/2)+...+1/((1+33)*33/2)
=2*(1/(1*2)+1/(2*3)+1/(3*4)...+1/(33*34))
=2*((1-1/2)+(1/2-1/3)+(1/3-1/4)...+(1/33-1/34))
=2*(1-1/34)
=33/17