计算
问题描述:
计算
1 1 1 1 1
----- + ----- + ----- + ------ + …… + ------
1*3 2*4 3*5 4*6 18*20
答
原式=(1/2)*(1- 1/3)+ (1/2)*(1/2 - 1/4) + (1/2)*(1/3 - 1/5) + (1/2)*(1/4 - 1/6) +.+ (1/2)*(1/17 - 1/19) + (1/2)*(1/18 - 1/20) =(1/2)*[(1- 1/3)+(1/3 - 1/5) +.+(1/17 - 1/19)+ (1/2 - 1/4) + (1/4 - 1/6) +....为什么要有(1/2)因为 1- 1/3=2/3,1/3 - 1/5=2/15,而 1/(1*3)=1/3,1/(3*5)=15所以:(1/2)*(1- 1/3)=1/(1*3),(1/2)*(1/3 - 1/5)=1/(3*5)依此类推