Question

New fun binomial question!!

Answer 1

Let \[1+\sum_{r=1}^{10}\left( 3^r.~^{10}C_r+r.~^{10}C_r \right)=2^{10}\left( \alpha.4^5+\beta \right)\]where \(\alpha,~\beta \in N\) and \(f(x)=x^2-2x-k^2+1\). If \(\alpha,~\beta\) lies between the roots of \(f(x)=0\). Then find the smallest integral value of \(k\).

Answer 2

@dan815

Answer 3

Is this the same thing? \[~^{10}C_r = \binom{10}{r}\]

Answer 4

yes