Question

在数列an中,若a1=2,na(n+1)=(n+1)an+2(n属于N*),则a10等于

如题，答案是38，
详细的解题过程，谢谢了

Answer 1

na(n+1)=(n+1)an+2 (两边同除以n(n+1) )
a(n+1)/(n+1)=an/n+2/n(n+1)
a(n+1)/(n+1)-an/n=2[1/n-1/(n+1)]
a2/2-a1/1=2(1-1/2)
a3/3-a2/2=2(1/2-1/3)
;
a10/10-a9/9=2(1/9-1/10)
上式相加得
a10/10-a1/1=2(1-1/2+1/2-1/3+...+1/9-1/10)
a10/10-2=2(1-1/10)
a10/10-2=9/5
解得a10=38

Answer 2

bn=an/n+2/n
b(n+1)=bn
b1=2+2=4
b10=4=a10/10+0.2
a10=38