a, S = 2 + $2^{2}$ + $2^{3}$ + ..... + $2^{24}$
= ( 2 + $2^{2}$ ) + ( $2^{3}$ + $2^{4}$ ) + ...... + ( $2^{23}$ + $2^{24}$ )
= 2 . ( 1 + 2 ) + $2^{3}$ . ( 1 + 2 ) + ...... + $2^{23}$ . ( 1 + 2 )
= 3 . 2 + 3 . $2^{3}$ + ..... + 3 . $2^{23}$
= 3. ( 2 + $2^{3}$ + .....+ $2^{23}$ ) ⁝ 3 ( 1 )
b, Có S = 2 + $2^{2}$ + $2^{3}$ + ...... + $2^{24}$
⇒ S = 2 . ( 1 + 2 + $2^{2}$ + ..... + $2^{23}$ ) ⁝ 2 ( 2 )
Từ ( 1 ) và ( 2 ) ⇒ S ⁝ 6
⇒ S là bội của 6
c, S = 2 + $x2^{2}$ + ..... + $2^{24}$
⇒ 2S = $2^{2}$ + $2^{3}$ + ..... + $2^{25}$
⇒ 2S - S
S = $2^{25}$ - 2 < $2^{25}$
