Question

[Thiên Thiên]

Cho B=1+2+2^2+...+2^19

Hỏi B chia cho 7 dư bn?

#cầu_trả_lời

Answer 1

[Carol]

B = \(1+2+2^2+2^3+2^4+2^5+.....+2^{17}+2^{18}+2^{19}\)

=\(\left(1+2+2^2\right)+\left(2^3+2^4+2^5\right)+.....+\left(2^{17}+2^{18}+2^{19}\right)\)

=\(1.\left(1+2+2^2\right)+2^3.\left(1+2+2^2\right)+.....+2^{17}.\left(1+2+2^2\right)\)

=\(1.\left(7\right)+2^3.\left(7\right)+......2^{17}.\left(7\right)\)

=\(\left(1+2^3+.....+2^{17}\right).7\)Thì chia hết cho 7 và không có dư

Ticks mình nhé!

Answer 2

[Hồng Nhan]

B = 1 +2 +2^2 + ......+ 2^19

2B = 2 . ( 1 + 2 + 2^2 + ......+ 2^19 )

2B = ( 2 + 2^2 + 2^3 + ......+ 2^19 + 2^20 )

2B - B = ( 2 + 2^2 + 2^3 + ......+ 2^19 + 2^20 ) - ( 1 +2 +2^2 + ......+ 2^19 )

2B - B = 2^20 - 1

B = 2^20 - 1