Question

2.2^2+3.2^3+4.2^4+...+(n-1).2^n-1+n.2^n=2^n+34 tìm n

Answer 1

Lời giải:

$2^n+34=2.2^2+3.2^3+....+n.2^n$

$2^{n+1}+68=2.2^3+3.2^4+....+n.2^{n+1}$

Trừ theo vế:

$2^n+34=n.2^{n+1}-(8+2^3+2^4+...+2^n)$

$n.2^{n+1}-2^n-42=2^3+2^4+...+2^n$

$n.2^{n+2}-2^{n+1}-84=2^4+....+2^{n+1}$

Trừ theo vế:

$n.2^{n+1}-2^n-42=2^{n+1}-8$

$2^n(2n-3)=34=17.2$

$\Rightarrow 2^n=2$ và $2n-3=17$ (vô lý)

Vậy không tìm được $n$.