简算题(奥数题): 1⼀1+2+1⼀1+2+3+1⼀1+2+3+4+1⼀1+2+3+4+5…+1⼀1+2+3+4+5+…+35

(1-1⼀2×2)×(1-1⼀3×3)×(1-1⼀4×4)×(1-1⼀59×59)×(1-1⼀60×60)
2024-12-01 02:53:08
推荐回答(1个)
回答1:

1/1+2+1/1+2+3+1/1+2+3+4+1/1+2+3+4+5…+1/1+2+3+4+5+…+35
=1/3+1/6+1/10+1/15+...+1/630
=2×(1/6+1/12+1/20+1/30+...+1/1260
=2×(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/35-1/36)
=2×(1/2-1/36)
=2×17/36
=17/18