Đáp án:
$S = \dfrac{n+3}{6}$
Giải thích các bước giải:
phân tích :
$\dfrac{C_n^k}{C_{n+2}^{k+1}} = \dfrac{n!}{(n-k)!k!}. \dfrac{(k+1)!(n-k+1)!}{(n+2)!}$
$= \dfrac{(n-k+1)(k+1)}{(n+2)(n+1)}$
$= \dfrac{nk+n-k^2 +1}{(n+2)(n+1)}$
$\longrightarrow S = \dfrac{n.1+1-0+2n+1-1^2+3n+1-2^2+.....+n(n+1)+1-n^2}{(n+1)(n+2)}$
$= \dfrac{n(1+2+3+....n+1)+n+1-(1^2+2^2+....n^2)}{(n+1)(n+2)}$
$= \dfrac{n+3}{6}$
