Question

2乘3分之1加3乘4分之一加4乘5分之一.依次加到50乘51分之最后等于多少?急 .

Answer 1

1/(2*3)+1/(3*4)+1/(4*5)+……+1/（50*51)

=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)……+(1/50-1/51)

=1-1/51

=50/51

1/(2*3)+1/(3*4)+1/(4*5)+……+1/[n*(n+1)]

=n/(n+1)