Question

Cho B=3+3²+3³+.....+3⁶⁰.Chứng minh rằng A chia hết cho 4;chia hết cho 13

Answer 1

B=(3+3²+3³)+(3⁴+3⁵+3⁶)+...+(3⁵⁸+3⁵⁹+3⁶⁰)

=3(1+3+9)+3⁴(1+3+9)+...+3⁵⁸(1+3+9)

=13.3+13.3⁴+...+13.3⁵⁸

=13.(3+3⁴+...+3⁵⁸) luôn chia hết cho 13

vậy B chia hết cho 13

Answer 2

B=(3+3²)+(3³+3⁴)+...+(3⁵⁹+3⁶⁰)

B=3(1+3)+3³(1+3)+3⁴(1+3)+...+3⁵⁹(1+3)

4(4+3³+3⁴+...+3⁵⁹)

suy ra:4(4+3³+3⁴+...+3⁵⁹)chia hết cho 4

 

Answer 3

ta có :(3^1+3^2+3^3)+(3^4+3^5)+.......+(3^58+3^59+3^60)
=(3+9+27)+3^4.(3+9+27)+.......+3^58.(3+9+27)
=39+3^4.39+.......+3^58.39
=39.(3^1+3^4+..........+3^58) chia het cho 13
(Vi 39 chia het cho 13 )
Vậy A chia hết cho 13
thanks