Question

3Q,怎么简便2/3+2/15+2/35+2/63+2/99+2/143+2/195+2/255+2/323+2/399

Answer 1

2/(n-1)(n+1)=1/(n-1)-1/(n+1)

2/3+2/15+2/35+2/63+2/99+2/143+2/195+2/255+2/323+2/399

=1-1/3+1/3-1/5+1/5-1/7+-----------+1/19-1/21

=1-1/21

=20/21