Задача 68542 Используйте следующую формулу для суммы...
Условие
Решение
[m](1+x)^{-4}=1-4х + \frac{(-4)(-4-1)}{2!}x^2+\frac{(-4)(-4-1)(-4-2)}{3!}x^3+\frac{(-4)(-4-1)(-4-2)(-4-3)}{4!}x^4 + ...[/m]
б) Подставляем в формулу m=1/3
[m](1+x)^{\frac{1}{3}}=1+\frac{1}{3}х + \frac{\frac{1}{3}(\frac{1}{3}-1)}{2!}x^2+\frac{\frac{1}{3}(\frac{1}{3}-1)(\frac{1}{3}-2)}{3!}x^3+\frac{\frac{1}{3})(\frac{1}{3}-1)(\frac{1}{3}-2)(\frac{1}{3}-3)}{4!}x^4 + ...[/m]
или
m=1/5
[m](1+x)^{\frac{1}{5}}=1+\frac{1}{5}х + \frac{\frac{1}{5}(\frac{1}{5}-1)}{2!}x^2+\frac{\frac{1}{5}(\frac{1}{5}-1)(\frac{1}{5}-2)}{3!}x^3+\frac{\frac{1}{5})(\frac{1}{5}-1)(\frac{1}{5}-2)(\frac{1}{5}-3)}{4!}x^4 + ...[/m]
