1/1×3+1/3×5+1/5×7+1/7×9+1/9×11+1/11×13+1/13×15+1/15×17+1/17×19
问题描述:
1/1×3+1/3×5+1/5×7+1/7×9+1/9×11+1/11×13+1/13×15+1/15×17+1/17×19
答
1/1×3+1/3×5+1/5×7+1/7×9+1/9×11+1/11×13+1/13×15+1/15×17+1/17×19
=1/2*(1-1/3+1/3-1/5+1/5-1/7+.+1/17-1/19)
=1/2*(1-1/19)
=1/2*18/19
=9/19