Question

已知数列{an}满足:a1+a2+a3+…+an=n-an,

n=(1,2,3…)
求a1,a2,a3的值,

Answer 1

a1+a2+a3+…+an=n-an

1-a1=a1
a1=1/2

2-a2=a1+a2
2a2=2-a1=2-1/2=3/2
a2=3/4

3-a3=a1+a2+a3
2a3=3-(a1+a2)=3-(1/2+3/4)=(12-2-3)/4=7/4
a3=7/8