2∕3+14/15+34/35+62/63+98/99+142/143

问题描述:

2∕3+14/15+34/35+62/63+98/99+142/143

2∕3+14/15+34/35+62/63+98/99+142/143
=1-1/3+1-1/15+1-1/35+1-1/63+1-1/99+1-1/143
=6-(1/3+1/15+1/35+1/63+1/99+1/143)
=6-1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/14)
=6-1/2*(1-1/14)
=6-13/28
=5又15/28

2∕3+14/15+34/35+62/63+98/99+142/143
=6-(1/3+1/15+1/35+1/63+1/99+1/143)
=6-1/2*(2/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)
=6-1/2*(1-1/13)
=6-6/13
=5又7/13 .

2∕3+14/15+34/35+62/63+98/99+142/143
=6-(1/3+1/15+1/35+1/63+1/99+1/143)
=6-1/(5-3)×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)【裂项法,什么叫分裂啊】
=6-1/2×12/13
=6-6/13
=72/13(5又7/13)

=1—1/3+1—1/15+1—1/35+1—1/63+1—1/99+1—1/143
=6—(1/3+1/15+1/35+1/63+1/99+1/143)
=6-(1—1/3+1/3—1/5+1/5+-—1/7+1/7—1/9+1/9—1/11+1/11—1/13)÷2(分裂法)
=6—(1—1/13)÷2
=6—6/13
=5又7/13