Question

1乘3分之1+3乘5分之1+5乘7分之1+……+17乘19分之1+19乘21分之1,求等于多少?

Answer 1

1/1*3+1/3*5+.+1/19*21

=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/19-1/21]

=1/2*[1-1/3+1/3-1/5+.+1/19-1/21]

=1/2[1-1/21]

=10/21