2/3+2/3x5+2/5x7+2/7x9+2/9x11+2/11x13=?

2/3+2/3x5+2/5x7+2/7x9+2/9x11+2/11x13=?
2/3+2/3x5+2/5x7+2/7x9+2/9x11+2/11x13=?

2/3+2/3x5+2/5x7+2/7x9+2/9x11+2/11x13=?
2/3=1-1/3
2/3x5 = 1/3-1/5
2/5x7 = 1/5-1/7
2/7x9 = 1/7-1/9
2/9x11=1/9-1/11
2/11x13= 1/11-1/13
以上各式左右分别相加
原式=1-1/13=12/13

这要找规律，2/3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13=2/3+1/2*（2/3-2/5）+1/2*（2/5-2/7）+1/2
*（2/7-2/9）+1/2*（2/9-2/11）+1/2*（2/11-2/13）=2/3+1/2*（2/3-2/5+2/5-2/7+2/7-2/9+2/9-2/11+2/11-2/13）=2/3+1/2*（2/3-2/13）=2/3+10/39=108/117 =12/13