Question

若{an}中a1=1,an=an-1+n(n-1)分之1（n大于等于2）写出前5项和它的通项公式

Answer 1

an=a(n-1)+1/n(n-1)=a(n-1)+1/(n-1)-1/n

an+1/n=a(n-1)+1/(n-1)

a1+1=1+1=2

数列{an+1/n}是各项均等于2的常数数列.

an+1/n=2

an=2-1/n

a1=2-1=1,同样满足.

数列{an}的通项公式为an=2-1/n

a1=1

a2=2-1/2=3/2

a3=2-1/3=5/3

a4=2-1/4=7/4

a5=2-1/5=9/5