Question

若数列{an}满足a1=1,an+1=an+1/n(n+1),则an=?

我着急，请您快些

Answer 1

因为1/n(n+1)=1/n-1/(n+1)

an+1=an+1/n-1/(n+1)
an=an-1+1/(n-1)-1/n
...
a2=a1+1-1/2
全加

得
an+1=a1+1-1/(n+1)

所以an=2-1/n
不懂的可以和我说 我到时候告诉你~

Answer 2

a(n+1)=an+1/n-1/(n+1)
a(n+1)+1/(n+1)=an+1/n
令bn=an+1/n, 则b(n+1)=a(n+1)+1/(n+1)
所以b(n+1)=bn=b(n-1)=...=b1=2
所以bn=b1=2，而bn=an+1/n
所以an=2-1/n

Answer 3

1

Answer 4

您好！你应该把an和后面的一项写清楚