分からない問題はここに書いてね436

[D]

100*n - 50*i = 10*(10*n - 5*i)

両替に50円玉が i 枚含まれる両替の仕方の数は、

[C]より

[(10*n - 5*i) + 1]^2 通り

Σ [(10*n - 5*i) + 1]^2 from i = 0 to i = 2*n

=

Σ [(10*n - 5*i) + 1]^2 from i = 0 to i = 2*n

=

Σ [5*(2*n - i) + 1]^2 from i = 0 to i = 2*n

=

Σ [5*i + 1]^2 from i = 0 to i = 2*n