Toán Lớp 6: Không làm phép tính hãy chứng tỏ rằng tổng A chia hết cho 3: A=2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2¹⁰+2¹¹+2¹²+2¹³

Question

Toán Lớp 6:  Không làm phép tính hãy chứng tỏ rằng tổng A chia hết cho 3: A=2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2¹⁰+2¹¹+2¹²+2¹³

hatuanlan · Answer

A=2⁰+2+2&sup2;+2&sup3;+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2&sup1;⁰+2&sup1;&sup1;+2&sup1;&sup2;+2&sup1;&sup3;     A=(2⁰+2)+(2&sup2;+2&sup3;)+(2⁴+2⁵)+(2⁶+2⁷)+(2⁸+2⁹)+(2&sup1;⁰+2&sup1;&sup1;)+(2&sup1;&sup2;+2&sup1;&sup3;)     A=2⁰. (2⁰+2) + 2&sup2;.(1+2) + 2⁴.(2+4) + 2⁶.(2+4) + 2⁸.(2+4) + 2&sup1;⁰.(2+4)+2&sup1;&sup2;(2+4)     A=2⁰.3 + 2&sup2;.3 + 2⁴.3 + 2⁶.3 + 2⁸.3+ 2&sup1;⁰.3+2&sup1;&sup2;.3     A=(2⁰+2&sup2; + 2⁴ + 2⁶ + 2⁸+ 2&sup1;⁰+2&sup1;&sup2;).3     Ta thấy (2⁰+ 2&sup2; + 2⁴ + 2⁶ + 2⁸+ 2&sup1;⁰+2&sup1;&sup2;).3 chia hết cho 3 n&ecirc;n tổng A chia hết cho 3     Vậy tổng A  chia hết cho 3        Xin hay nhất           Admin đừng c&oacute; xo&aacute; :(

dananhthumai · Answer

A=2⁰+2+2&sup2;+2&sup3;+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2&sup1;⁰+2&sup1;&sup1;+2&sup1;&sup2;+2&sup1;&sup3;     A=(2⁰+2)+(2&sup2;+2&sup3;)+(2⁴+2⁵)+(2⁶+2⁷)+(2⁸+2⁹)+(2&sup1;⁰+2&sup1;&sup1;)+(2&sup1;&sup2;+2&sup1;&sup3;)     A=2⁰. (2⁰+2) + 2&sup2;.(1+2) + 2⁴.(2+4) + 2⁶.(2+4) + 2⁸.(2+4) + 2&sup1;⁰.(2+4)+2&sup1;&sup2;(2+4)     A=2⁰.3 + 2&sup2;.3 + 2⁴.3 + 2⁶.3 + 2⁸.3+ 2&sup1;⁰.3+2&sup1;&sup2;.3     A=(2⁰+2&sup2; + 2⁴ + 2⁶ + 2⁸+ 2&sup1;⁰+2&sup1;&sup2;).3     Ta thấy (2⁰+ 2&sup2; + 2⁴ + 2⁶ + 2⁸+ 2&sup1;⁰+2&sup1;&sup2;).3 chia hết cho 3 n&ecirc;n tổng A chia hết cho 3     Vậy tổng A  chia hết cho 3        Xin hay nhất