Question

已知等差数列an的首项a1>0,公差d>0,前n项和为Sn

Answer 1

Sn = d / 2 n^2 + (a1 - d / 2) n ,

(1).

Sn + Sm = d / 2 (n^2 + m^2) + (a1 - d / 2) (n + m)

>= d / 2 (n^2 + m^2 + 2 n m) / 2 + (a1 - d / 2) (n + m)

= d / 2 2 p^2 + (a1 - d / 2) 2 p

= 2 [d / 2 p^2 + (a1 - d / 2) p]

= 2 Sp

(2.)

Sn Sm = d^2 / 4 m^2 n^2 + (a1 - d / 2)^2 m n + d / 2 (a1 - d / 2) m n (m + n)

= d^2 / 4 [√(m n)]^4 + (a1 - d / 2)^2 [√(m n)]^2 + d / 2 (a1 - d / 2) [√(m n)]^2 (m + n)