在数列{an}中,a1=2,nan+1=(n+1)an+2(n∈N*),则a10为(  ) A.34 B.36 C.38 D.40

问题描述:

在数列{an}中,a1=2,nan+1=(n+1)an+2(n∈N*),则a10为(  )
A. 34
B. 36
C. 38
D. 40

∵nan+1=(n+1)an+2∴

an+1
n+1
an
n
2
n(n+1)
=2(
1
n
 −
1
n+1
)
a10
10
a10
10
a9
9
+
a9
9
a8
8
+…+
a2
2
a1
1
+a1

=2[(
1
9
1
10
)+(
1
8
1
9
)+…+(1-
1
2
)]+2=
38
10

a10=38
故选C.