A=(2+22+23+24)+(257+258+259+260)

A=2(1+2+22+23)+...+257(1+2+22+23)

A=(1+2+22+23)(1+...+257)=15(1+...+257)⋮15

Bài 5. Có 16 con bò. Số trâu nhiều hơn số bỏ là 14 con. Hỏi có bao nhiêu con trâu?

A=(2+22+23+24)+(257+258+259+260)

A=2(1+2+22+23)+...+257(1+2+22+23)

A=(1+2+22+23)(1+...+257)=15(1+...+257)⋮15

Lời giải:

$A=(2+2^2+2^3)+(2^4+2^5+2^6)+....+(2^{58}+2^{59}+2^{60})$

$=2(1+2+2^2)+2^4(1+2+2^2)+....+2^{58}(1+2+2^2)$

$=(1+2+2^2)(2+2^4+....+2^{58})$

$=7(2+2^4+....+2^{58})\vdots 7$.

A = 2+2²+2³+...+2⁶⁰

A = 2.(1+2+2²) + 2⁴.(1+2+2²) + ... + 2⁵⁸.(1+2+2²)

A = 2.7+2⁴.7+...+2⁵⁸.7

A= 7. (2+2⁴+...+2⁵⁸) chia hết cho 7

--> A chia hết cho 7 (ĐPCM)

Ta có:

\(H=2+2^2+2^3+...+2^{60}\)

\(H=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

\(H=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\cdot\left(1+2\right)\)

\(H=3\cdot\left(2+2^3+...+2^{59}\right)\)

Vậy H chia hết cho 3

_______

\(H=2+2^2+2^3+...+2^{60}\)

\(H=\left(2+2^2+2^3\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)

\(H=2\cdot\left(1+2+4\right)+2^4\cdot\left(1+2+4\right)+...+2^{58}\cdot\left(1+2+4\right)\)

\(H=7\cdot\left(2+2^4+...+2^{58}\right)\)

Vậy H chia hết cho 7

__________

\(H=2+2^2+2^3+...+2^{60}\)

\(H=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+...+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)

\(H=2\cdot\left(1+2+4+8\right)+2^5\cdot\left(1+2+4+8\right)+...+2^{57}\cdot\left(1+2+4+8\right)\)

\(H=15\cdot\left(2+2^5+...+2^{57}\right)\)

Vậy H chia hết cho 15 

$H=2+2^2+2^3+\mathrm{...}+2^{60}$

Ta có:

 $H=2.\left(1+2\right)+2^3.\left(1+2\right)+\mathrm{...}+2^{59}.(1+2)$

 $H=2.3+2^3.3+\mathrm{...}+2^{59}.3$

$H=3.\left(2+2^3+\mathrm{...}+2^{59}\right)⋮3$

Ta có:

 $H=2.\left(1+2+2^2\right)+2^4.\left(1+2+2^2\right)+\mathrm{...}+2^{28}.\left(1+2+2^2\right)$

hoho

chỉ có làm thì mới có ăn

ko giúp thì  đừng nhắn thế

A= (2+22)+(23+24)+...+(259+260)
A=2.(1+2)+23.(1+2)+...+259.(1+2)
A=2.3+23.3+...+259.3
A=3.(2+23+...+259)
Vì 3 chia hết cho 3 => 3.(2+23+...+259)  chia hết cho 3
=>A  chia hết cho 3
A= (2+22+23)+...+(258+259+260)
A=2.(1+2+22)+...+258.(1+2+22)
A=2.7+...+258.7
A=7.(2+...+258)
Vì 7  chia hết cho 7 =>7.(2+...+258)  chia hết cho 7

CHIA HẾT CHO 3 :

A= (2+22)+(23+24)+...+(259+260)

A=2.(1+2)+23.(1+2)+...+259.(1+2)

A=2.3+23.3+...+259.3

A=3.(2+23+...+259)

Vì 3 chia hết cho 3 => 3.(2+23+...+259) chia hết cho 3

=>A chia hết cho 3

dcv