k - (1/2) k (k + 1)
= - (1/2) k (- 2 + (k + 1))
= - (1/2) k (k - 1)
= - (1/2) (k-1) k
= - (1/2) (k-1) ((k-1) + 1)
1 + 2 + ‥‥ + (n-2) + (n-1) + n - (1/2) n (n + 1)
= 1 + 2 + ‥‥ + (n-2) + (n-1) - (1/2) (n-1) ((n-1) + 1)
= 1 + 2 + ‥‥ + (n-2) - (1/2) (n-2) ((n-2) + 1)
‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥
‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥
= 1 + 2 - (1/2) 2 (2 + 1)
= 1 - (1/2) 1 (1 + 1) = 1 - 1 = 0
よって、
1 + 2 + ‥‥ + (n-2) + (n-1) + n = (1/2) n (n + 1)
最新の画像［もっと見る］
