0 votes 0 votes Find closed form for the generating function of the following sequence $\binom{7}{0}, \binom{7}{1}, \binom{7}{2}, ......., \binom{7}{7},0,0,0,0,0,...$ Combinatory generating-functions discrete-mathematics kenneth-rosen + – Mk Utkarsh asked Oct 12, 2018 edited Mar 3, 2019 by Pooja Khatri Mk Utkarsh 444 views answer comment Share Follow See 1 comment See all 1 1 comment reply !KARAN commented Dec 2, 2018 reply Follow Share $\binom{7}{0}, \binom{7}{1}, \binom{7}{2}, ......., \binom{7}{7} $ After this when lower value increases it becomes $\binom{7}{7+k}$ where $k \geq 1$, then all of them becomes $0$. so the given series is the expansion of $(1+x)^7$ using extended binomial theorem 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes 7^c_0+7c1x+7c2*x^2+7c3*x^3+7c4*x^5+7c6*x^6+7c7*x^7....rest terms 0 so closed form will be $(1+x)^7$ Navneet Kalra answered Oct 12, 2018 edited Oct 13, 2018 by Mk Utkarsh Navneet Kalra comment Share Follow See all 0 reply Please log in or register to add a comment.