已知数列{an}满足a1=1且(n+2)a下标n+1=n下标an则a10的值是
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已知数列{an}满足a1=1且(n+2)a下标n+1=n下标an则a10的值是
a(n+1) / a(n) = n / (n+1)
a(n) / a(n-1)= (n-1) / n
a(n-1)/ a(n-2)= (n-2)/(n-1)
...
a3 / a2 = 2 / 3
a2 / a1 = 1 / 2
累乘:
a(n) / a1 = 1 / n
a(n) = 1 / n
a10 = 1/10
再问: 正确的答案是1/55.....
再答: a(n+1) / a(n) = n / (n+2) a(n) / a(n-1)= (n-1) / (n+1) a(n-1)/ a(n-2)= (n-2) / n a(n-2)/ a(n-3)= (n-3) / (n-1) a(n-3)/ a(n-4)= (n-4) / (n-2) ... a5 / a4 = 4 / 6 a4 / a3 = 3 / 5 a3 / a2 = 2 / 4 a2 / a1 = 1 / 3 累乘:(隔项相消) a(n) / a1 = 2 / n(n+1) a(n) = 2 / n(n+1) a10 = 1/55 方法都一样......
再问: 谢谢您!!!
a(n) / a(n-1)= (n-1) / n
a(n-1)/ a(n-2)= (n-2)/(n-1)
...
a3 / a2 = 2 / 3
a2 / a1 = 1 / 2
累乘:
a(n) / a1 = 1 / n
a(n) = 1 / n
a10 = 1/10
再问: 正确的答案是1/55.....
再答: a(n+1) / a(n) = n / (n+2) a(n) / a(n-1)= (n-1) / (n+1) a(n-1)/ a(n-2)= (n-2) / n a(n-2)/ a(n-3)= (n-3) / (n-1) a(n-3)/ a(n-4)= (n-4) / (n-2) ... a5 / a4 = 4 / 6 a4 / a3 = 3 / 5 a3 / a2 = 2 / 4 a2 / a1 = 1 / 3 累乘:(隔项相消) a(n) / a1 = 2 / n(n+1) a(n) = 2 / n(n+1) a10 = 1/55 方法都一样......
再问: 谢谢您!!!
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