Question

HÃY CHỨNG MINH RẰNG

A=2+2 mũ 2+2 mũ 3 + 2 mũ 4+...+2 mũ 100 chia hết cho 31

CÁC BN GIÚP MK NHA AI ĐÚNG MK CHO 3 TK 

CẢM ƠN TRƯỚC NHA CÁC THIÊN TÀI TOÁN HK GIÚP MK

Answer 1

Co Gai De Thuong

A = 2 + 2² + 2³ + ... + 2⁹⁹ + 2¹⁰⁰

   = ( 2 + 2² + 2³ + 2⁴ + 2⁵ ) + ... + ( 2⁹⁶ + 2⁹⁷ + 2⁹⁸ + 2⁹⁹ + 2¹⁰⁰ )

   = 2 x ( 1 + 2 + 2² + 2³ + 2⁴ ) + ... + 2⁹⁶ x  ( 1 + 2 + 2² + 2³ + 2⁴ )

   = 2 x      31                          + ... +  2⁹⁶ x 31

   = 31 ( 2 + ... + 2⁹⁶ )

Vậy A chia hết cho 31       

Answer 2

A = 2 + 2² + 2³ + 2⁴ + 2⁵ + .... + 2⁹⁶ + 2⁹⁷ + 2⁹⁸ + 2⁹⁹ + 2¹⁰⁰

A = [2 + 2² + 2³ + 2⁴ + 2⁵] + ... + 2⁹⁵[2 + 2² + 2³ + 2⁴ + 2⁵]

A = 62 + ... + 2⁹⁵.62

A = 2.31 + .... + 2⁹⁵.2.31

A = 31.2.[2⁰ + 2⁵ + ... +2⁹⁵]

=> A \(⋮31\)

Answer 3

Ta có
\(A=2^1+2^2+2^3+...+2^{100}\)
\(A=\left(2^1+2^2+2^3+2^4+2^5\right)+....+\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)\)
\(A=2\left(1+2+2^2+2^3+2^4\right)+...+\left(1+2+2^2+2^3+2^4\right)\left(2^{96}+2^{96}+2^{96}+2^{96}\right)\)
\(A=\left(1+2^2+2^3+2^4+2^5\right)\left(2+...+2^{96}\right)\)
\(A=31.\left(2+...+2^{96}\right)⋮31\)

Answer 4

A=2+2^2+2^3 + 2^4+...+2^100

A= 2( 1+2+2^2+2^3+...+ 2^99)

A= 2[ (1+2+2^2+2^3+2^4)+...+(2^94 +2^95+ 2^96+2^97+2^99) ]

A= 2 [ 31 +...+ 2^94(1+2+2^2+2^3+2^40]

A= 2[( 31+...+ 2^99. 31)

A= 2 [ 31 .( 2^5 + 2^10+ ... + 2^94)] chia hết cho 31 

=> A chia heetrs cho 31

Answer 5

Ah mik nhầm bước 3 nhé
Sửa thành
\(A=2\left(1+2+2^2+2^3+2^4+2^5\right)+...+\left(1+2+2^2+2^3+2^4+2^5.2^{96}\right)\)
 

Answer 6

Co Gai De Thuong

<br class="Apple-interchange-newline"><div id="inner-editor"></div>C=2+22+23+...+299

C=(2+22+23+24+25)+...+(296+297+298+299+2100)

C=2(1+2+22+23+24)+...+296(1+2+22+23+24)

C=2.31+...+296.31

C = 31(2+...+2⁹⁶) chia hết cho 31

Answer 7

Thành viên

Con mất dậy,đồ copy