已知各项均为正数的无穷数列{a_n }满足a_(n+1)+a_n=2n,且a1=0.5,怎么求通项公式

2025-05-13 23:20:42
推荐回答(1个)
回答1:

a1=1/2
a(n+1)+an=2n

a(n+1) -(n+1) +1/2 = - ( an -n + 1/2 )

=> {an -n + 1/2} 是等比数列, q=-1
an -n + 1/2 = (-1)^(n-1) .(a1 -1 + 1/2)
an = n - 1/2