3/1+5/1+7/1+……+399/1=?

问题描述:

3/1+5/1+7/1+……+399/1=?

1×2/1+2×3/1+3×4/1+……+99×100/1
=1-2/1+2/1-3/1+3/1-4/1+……+99/1-100/1
=1-100/1
=100/99
3×5/1+5×7/1+7×9/1+……+97×99/1
=2/1×(3/1-5/1+5/1-7/1+7/1-9/1+……+97/1-99/1)
=2/1×(3/1-99/1)
=99/16