由于{an}和{bn}是等差数列 所以有 an+a(n+2)=2a(n+1) bn+b(n+2)=2b(n+1) 上面两式相加得到 an+a(n+2)+bn+b(n+2)=2a(n+1)+2b(n+1) an+bn+a(n+2)+b(n+2)=2[a(n+1)+b(n+1)] 设cn=an+bn 则有 cn+c(n+2)=2c(n+1) 所以{an+bn}是等差数列
