1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)的简便计算的过程

Question

问题要求详细！！！！！！！！！！！！！！！！！！！！！！有奖！！！！

Answer 1

原式=1-1/2+1/2-1/3……
即1/(n*(n+1))=1/n-1/(n+1)
所以原式=1-1/5=4/5.

Answer 2

1/1*2+1/2*3+1/3*4+1/4*5
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/2+1/2+1/3-1/3+1/4-1/4-1/5
=1-1/5
=4/5

Answer 3

1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
1/4*5=1/4-1/5
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/2+1/2+1/3-1/3+1/4-1/4-1/5
=1-1/5
=4/5

Answer 4

1-1/2+1/2-1/3+1/3-1/4+1/4-1/5=1-1/5=4/5