a)A=2+2^2+2^3+...+2^60 chia hết cho 15

=>(2+2^2+2^3+2^4)+...+(2^57+2^58+2^59+2^60)

=>2.(1+2+2^2+2^3)+...+2^57+(1+2+2^2+2^3)

=>2.15+...+2^57.15

Vì 15 chia hết choo 15

=>a chia hết cho 15

b)B=1+5+5^2+5^3+...+5^56+5^59+5^98 chia hết cho 31

=>(1+5+5^2)+...+5^56.(1+5+5^2)

=>31+....+5^56.3vi2 31 chia hết cho 31

=>B chia hết cho 31

Ta có : 
=2+2^2+2^3+...+2^60 = 2(1+2+2^2+2^3) + 2^5(1+2+2^2+2^3) + ... + 2^57(1+2+2^2+2^3) 
A=(2+2^5+...+2^57)*15 chia het cho 15 

A = 2 + 2² + 2³ + ... + 2⁵⁶

= (2 + 2² + 2³ + 2⁴) + (2⁵ + 2⁶ + 2⁷ + 2⁸) + ... + (2⁵³ + 2⁵⁴ + 2⁵⁵ + 2⁵⁶)

= 30 + 2⁴.(2 + 2² + 2³ + 2⁴) + ... + 2⁵².(2 + 2² + 2³ + 2⁴)

= 30 + 2⁴.30 + ... + 2⁵².30

= 30.(1 + 2⁴ + ... + 2⁵²)

= 5.6.(1 + 2⁴ + ... + 2⁵²) ⋮ 5

Vậy A ⋮ 5

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

a) /-28/ + (-42) = 28 +(-42) = -14

b) đặt S = 7⁶+7⁵+7⁴+7³+7²+7

7S = 7^7+7^6+7^5+7^4+7^3+7^2

7S-S= (7^7+7^6+7^5+7^4+7^3+7^2) - ( 7⁶+7⁵+7⁴+7³+7²+7)

6S = 7⁷-7 = 823536

S = 823536:6 =137256

Dễ vậy mà ko bít

Làm thử coi

Cho A = 2 + 2² + 2³ + ... + 2⁵⁶ . Chứng tỏ rằng A chia hết cho 5.

A = ( 2 + 2² + 2³ + 2⁴ ) + ( 2⁵ + 2⁶ + 2⁷ + 2⁸ ) + ... + ( 2⁵³ + 2⁵⁴ )

A = 30 + ( 30 . 2⁴ ) + ... + ( 3 . 2⁵² )

A = 30 . ( 1 + 2⁴ + ... + 2⁵² )

Do 30 chia hết cho 5

=> 30 . ( 1 + 2⁴ + ... + 2⁵² ) chia hết cho 5

Vậy A chia hết cho 5

a) \(\left(1+2+2^2+...+2^7\right)\)

\(=\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^6+2^7\right)\)

\(=\left(1+2\right)+2^2.\left(1+2\right)+...+2^6.\left(1+2\right)\)

\(=3+2^2.3+...+2^6.3\)

\(=3.\left(1+2^2+...+2^6\right)⋮3\left(đpcm\right)\)

a) Đặt A = 1 + 2 + 2² + 2³ + ... + 2⁷

Ta có:

A = 1 + 2 + 2² + 2³ + ... + 2⁷

\(\Rightarrow\)2A = 2 + 2² + 2³ + 2⁴ + ... + 2⁸

\(\Rightarrow\)A = 2⁸ - 1 = 255

Vì 255\(⋮\)3\(\Rightarrow\)2 + 2² + 2³ + 2⁴ + ... + 2⁸\(⋮\)3

\(\Rightarrow\)ĐPCM