Give a formula for the coefficient of x^k in the expansion of (x^2 - 1/x)^100, where k is an integer. ( x^8 means x to the power of 8, ^ means to the power of).
Give a formula for the coefficient of x^k in the expansion of (x^2 - 1/x)^100, where k is an integer. ( x^8 means x to the power of 8, ^ means to the power of).
Use the binomial theorem:
$\displaystyle (a + b)^n = \sum_{k = 0}^n {n \choose k} a^{n-k}b^k$
So here we have $\displaystyle a = x^2$ and $\displaystyle b = \frac{1}{x}$. You do the rest.