Question

1/2*4+1/4*6+1/6*8+…+1/18*20

Answer 1

解由1/2*4=1/2(1/2-1/4)

1/4*6=1/2(1/4-1/6)

1/6*8=1/2(1/6-1/8)

.

1/18*20=1/2(1/18-1/20)

故1/2*4+1/4*6+1/6*8+…+1/18*20

=1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+.+1/2(1/18-1/20)

=1/2(1/2-1/4+1/4-1/6+1/6-1/8+.+1/18-1/20)

=1/2(1/2-1/20)

=1/2*9/20

=9/40