Question

3×5分之一+5×7分之一+7×9分之一+......+21×23分之一

Answer 1

=1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+...+1/2(1/19-1/21)+1/2(1/21-1/23)=(1/6-1/10)+(1/10-1/14)+(1/14-1/19)+..(1/38-1/42)+(1/42-1/46)(中间的可以全部抵消)=1/6-1/46=10/69