3/2*5+3/5*8+3/8*11+3/11*14+3/14*17
问题描述:
3/2*5+3/5*8+3/8*11+3/11*14+3/14*17
答
3/5*3/8+3/8*3/11+3/11*3/14+3/14
=9*[1/(5*8)]+9*[1/(8*11)]+9*[1/(11*14)]+3/14
=9[(1/3)*(1/5-1/8)+(1/3)*(1/8-1/11)+(1/3)*(1/11-1/14)]+3/14
=9*(1/3)*(1/5-1/8+1/8-1/11+1/11-1/14)+3/14
=3*(1/5-1/14)+3/14
=3/5-3/14+3/14
=3/5