(1-1/2×2)×(1-1/3×3)×(1-1/4×4)×(1-1/59×59)×(1-1/60×60)
(1-1/2×2)×(1-1/3×3)×(1-1/4×4)×(1-1/59×59)×(1-1/60×60)
追答(1-1/2×2)×(1-1/3×3)×(1-1/4×4)×...×(1-1/59×59)×(1-1/60×60)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/59)(1+1/59)(1-1/60)(1+1/60)
=1/2×3/2×2/3×4/3×3/4×5/4×...×58/59×60/59×59/60×61/60
=1/2×61/60 (中间部分分子分母一一约分,只剩下1/2和61/60)
=61/120
用到公式:a²-b²=(a-b)(a+b)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/59)(1+1/59)(1-1/60)(1+1/60)中间省略的是乘号么?
追答是的,都是相乘
追问这个结果我记得好像是0的诶……
追答绝对不是0
(1-1/2×2)×(1-1/3×3)×(1-1/4×4)×(1-1/59×59)×(1-1/60×60)
=(1-1/2²)×(1-1/3²)×(1-1/4²)×(1-1/59²)×(1-1/60²)
用公式: a²-b²=(a-b)(a+b)
1-1/2²=(1-1/2)(1+1/2)
1-1/3²=(1-1/3)(1+1/3)
...
然后约分.