09/09/28 14:27:15
>>489 (下)
S_k = [kx] - (2/(k+1))･([x] + [2x] + …… + [kx])
= (1/(k+1))･Σ(j=0,k) ([kx] - [jx] - [(k-j)x])
≧ 0,
とおくと
(左辺) - (右辺) = [nx] - Σ(k=1,n) [kx] /k
= … …
= (1/(n+1))Σ(k=0,n) ([nx] - [kx] - [(n-k)x]) + Σ(0<i+j≦n) (2/(i+j)(i+j+1))([(i+j)x] - [ix] - [jx])
= S_n + Σ(k=1,n) S_k /k
≧ 0,
ぬるぽ