1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8------1/17*19+1/18*20 如何用简便方法计算?

1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8------1/17*19+1/18*20 如何用简便方法计算?
1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8------1/17*19+1/18*20 如何用简便方法计算?

1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8------1/17*19+1/18*20 如何用简便方法计算?
=1/2[(1-1/3)+(1/2-1/4)+(1/3-1/5)+.+(1/17-1/19)+(1/18-1/20)
=1/2[1+1/2-1/3+1/3-1/4+1/4-.-1/18+1/18-1/19-1/20]
=1/2(1+1/2-1/19-1/20)
=(1/2)*(531/380)
=531/760