4/3+16/15+36/35+64/63+100/99+144/143=?
问题描述：
4/3+16/15+36/35+64/63+100/99+144/143=?
答
原式=1+1／3+1+1／15+1+1／35+1+1／63+1+1／99+1+1／143
=6+½[(1-1／3)+(1／3-1／5)+(1／5-1／7)+(1／7-1／9)+(1／9-1／11)+(1／11－1／13)]
=6+½[1-1／13】
=6+6／13
=6又6／13
答
=(1-1/3)+(1-1/3*5)+(1-1/5*7)+……+(1-1/11*13)
=6-[1/3+1/3*5+1/5*7+……+1/11*13]
=6-[(1/2)(1-1/3)+(1/2)(1/3-1/5)+(1/2)(1/5-1/7)+……(1/2)(1/11-1/13)]
=6-(1/2)(1-1/13)
=6-6/13
=72/13
答
原式=1+1/3+1+1/15+1+1/35+……+1+1/143
=6+1/2×（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13）
=6+1/2×（1-1/13）
=6又6/13