1⼀3+1⼀8+1⼀15+1⼀24……+1⼀320

2024-12-23 02:37:39

推荐回答（3个）

回答1：

1/3+1/8+1/15+1/24……+1/120
=1/1×3+1/2×4+1/3×5+1/4×6……+1/120
=(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.......1/9-1/11+1/10-1/12)÷2
=(1+1/2-1/11-1/12)÷2
=175/264

回答2：

1/3+1/8+1/15+1/24……+1/360
=（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/18-1/20）÷2
=（1+1/2-1/19-1/20）÷2
=531/380÷2
=531/760

回答3：

1/(1×3)+1/(2×4)+1/(3×5)+1/(4×6)+……+1/(18×20)
=1/2×(1-1/3)+1/2×(1/2-1/4)+1/2×(1/3-1/5)+1/2×(1/4-1/6)+……+1/2×(1/18-1/20)
=1/2×(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/18-1/20)
=1/2×(1+1/2-1/19-1/20)
=1/2×(531/380)
=531/760