Question

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

数列问题求解啊！！！！！！！！！！！！！！

Answer 1

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

追问

正确的答案是1/55.....

追答

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......

追问

谢谢您！！！