: Tính tổng${{1.3}^{0}}{{.5}^{n-1}}C_{n}^{n-1}+{{2.3}^{1}}{{.5}^{n-2}}C_{n}^{n-2}+…+n{{.3}^{n-1}}{{5}^{0}}C_{n}^{0}$
C. $n{{.8}^{n-1}}$
B. $(n+1){{.8}^{n-1}}$C.$(n-1){{.8}^{n}}$
D. $n{{.8}^{n}}$
Hướng dẫn
Chọn A
Ta có: $VT=\sum\limits_{k=1}^{n}{k{{.3}^{k-1}}{{.5}^{n-k}}C_{n}^{n-k}}$
Mà $k{{.3}^{k-1}}{{.5}^{n-k}}C_{n}^{n-k}=n{{.3}^{k-1}}{{.5}^{n-k}}.C_{n-1}^{k-1}$
Suy ra: $VT=n({{3}^{0}}{{.5}^{n-1}}C_{n-1}^{0}+{{3}^{1}}{{.5}^{n-2}}C_{n-1}^{1}+…+{{3}^{n-1}}{{5}^{0}}C_{n-1}^{n-1})$
$=n{{(5+3)}^{n-1}}=n{{.8}^{n-1}}$