Đáp án:
2A = 2.$2^{3}$ + 3. $2^{4}$ + 4. $2^{5}$ +... + n. $2^{n+1}$
-A=A-2A = 2.$2^{2}$ + (3.$2^{3}$ - 2.$2^{3}$) + .... +( n-n+1) $2^{n}$ - n. $2^{n+1}$
= 2.$2^{2}$ + $2^{3}$ + $2^{4}$+ .... + $2^{n}$ - n. $2^{n+1}$
=> A = -2.$2^{2}$ - ( $2^{2}$ +$2^{3}$ + $2^{4}$+ .... + $2^{n+1}$) + (n+1). $2^{n+1}$
B = $2^{2}$+$2^{3}$ + $2^{4}$ + $2^{5}$ +... + $2^{n+1}$
2B = $2^{3}$ + $2^{4}$ + $2^{5}$ +... + $2^{n+2}$
B= 2B- B= $2^{n+2}$ - $2^{2}$
=> A = $2^{2}$ - $2^{n+2}$ -2.$2^{2}$ +(n+1). $2^{n+1}$
= (n+1). $2^{n+1}$ - $2^{n+2}$= (n+1-2). $2^{n+1}$= 2(n-1) $2^{n}$
=> 2(n-1) = $2^{34}$ => n = $2^{33}$ + 1
