第一题:2/3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13=?

问题描述:

第一题:2/3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13=?
第二题:1/2*5+1/5*8+1/8*11+1/11*14+1/14*17=?

第一题:2/3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13=?
=1-1/3+1/3-1/5+1/5-1/7+...+1/11-1/13
=1-1/13
=12/13
第二题:1/2*5+1/5*8+1/8*11+1/11*14+1/14*17=?
=1/3[1/2-1/5]+1/3[1/5-1/8]+...+1/3[1/14-1/17]
=1/3[1/2-1/5+1/5-1/8+...+1/14-1/17]
=1/3[1/2-1/17]
=5/34