Toán Lớp 6: Số dư của A chia cho 3 là:
A = 2 + $2^{2}$ + $2^{3}$ + $2^{4}$ + ….. + $2^{200}$
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Toán Lớp 6: Số dư của A chia cho 3 là:
A = 2 + $2^{2}$ + $2^{3}$ + $2^{4}$ + ….. + $2^{200}$
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$\text{Ta có :}$$\\$ $\text{A = 2 + $2^{2}$ + $2^{3}$ + … + $2^{200}$ }$$\\$ $\text{$\Rightarrow$ A = ( 2 + $2^{2}$ ) + ( $2^{3}$ + $2^{4}$ ) + … + ( $2^{199}$ + $2^{200} )$}$$\\$ $\text{$\Rightarrow$ A = 2 ( 1 + 2 ) + $2^{3}$ ( 1 + 2 ) + … + $2^{199}$ ( 1 + 2 )}$$\\$ $\text{$\Rightarrow$ A = 2 . 3 + $2^{3}$ . 3 + … + $2^{199}$ . 3}$$\\$ $\text{$\Rightarrow$ A = 3 ( 2 + $2^{3}$ + … + $2^{199}$ ) $\vdots$ 3}$$\\$ $\text{Vì A $\vdots$ 3 }$$\\$ $\text{Nên A chia 3 dư 0}$
A= 2 + 2^2 + 2^3 + 2^4 + … + 2^200
A= (2+ 2^2) + (2^3 + 2^4) +… + (2^199 + 2^200)
A= 2 ( 1 + 2) + 2^3 (1+2)+ …+ 2^199 (1+3)
A= 2. 3 + 2^3 .3 + … + 2^199. 4
A= 3 (2 + 2^3 + … + 2^199) chia hết cho 3
=> A chia hết cho 3