4/3+16/15+36/35+64/63+100/99怎么简算?

题目

4/3+16/15+36/35+64/63+100/99怎么简算?

答案

4/3+16/15+36/35+64/63+100/99
=5+（1/3+1/15+1/35+1/63+1/99）
=5+1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5+1/2(1-1/11)
=5+5/11
=60/11