Задача 69111 Задание: вычислить сумму номера г)...

63e5f55478ed3d23da2ca5f9

10.02.2023 10:45:45

Задание: вычислить сумму номера г)

5f3ea7e3faf909182968ddd9

10.02.2023 13:10:29

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∑^(k=18) _(k=0)(r-2)^(k)(b-r)^(19-r)C^(k)_(19)=[blue]C^(0)_(19)(r-2)^(0)(b-r)^(19)+C^(1)_(19)(r-2)^(1)(b-r)^(18)+...+C^(18)_(19)(r-2)^(18)(b-r)^(1)[/blue]


По формуле бинома:

[blue]C^(0)_(19)(r-2)^(0)(b-r)^(19)+C^(1)_(19)(r-2)^(1)(b-r)^(18)+...+C^(18)_(19)(r-2)^(18)(b-r)^(1)[/blue]+C^(19)_(19)(r-2)^(19)(b-r)^(0)=((r-2)+(b-r))^(19)

[blue]C^(0)_(19)(r-2)^(0)(b-r)^(19)+C^(1)_(19)(r-2)^(1)(b-r)^(18)+...+C^(18)_(19)(r-2)^(18)(b-r)^(1)[/blue]=((r-2)+(b-r))^(19)-C^(19)_(19)(r-2)^(19)(b-r)^(0)

[blue]C^(0)_(19)(r-2)^(0)(b-r)^(19)+C^(1)_(19)(r-2)^(1)(b-r)^(18)+...+C^(18)_(19)(r-2)^(18)(b-r)^(1)[/blue]=(b-2)^(19)-(r-2)^(19)


∑^(k=18) _(k=0)(r-2)^(k)(b-r)^(k-r)C^(k)_(19)=(b-2)^(19)-(r-2)^(19)