Question

1/2+5/6+11/12+19/20+.109/110的值是多少?

Answer 1

C

1/2+5/6+11/12+19/20+.109/110

=1-1/2+1-1/6+1-1/12+1-1/20+.+1-1/110

=10-(1/2+1/6+1/12+1/20+.+1/110)

=10-(1/1*2+1/2*3+1/3*4+1/4*5+.+1/10*11)

=10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/10-1/11)

=10-(1-1/11)

=10-10/11

=100/11