Good day please no hand wrinting please very important no ha

Good day please no hand wrinting please ...very important no hand writing

Find the values of extended binomial coefficients(-3 3) and (1/2 4).

Solution

For negative integer n and any integer k .nCk =(-1)^k ( -n+k-1 C k) if k>=0 ..............*.

We ve (-3C3) I,e n = -3 and k=3>0. So we can apply * I,e we have to put the values in *.we get

(-3C3) = (-1)(5C3)= - 10..... nCk= n!/k!(n-k)!

* holds even for complex n and k .we can solve 1/2 C 4 by using * as nck = n/k (n-1 C k-1) ,k not equal to 0