Question

Chứng minh rằng

B = 1+ 7 + 7² + 7³ + 7⁴ + ... + 7¹⁰¹

B chia hết cho 8

Answer 1

\(B=1+7+7^2+7^3+7^4+...+7^{101}\)

\(B=\left(1+7\right)+\left(7^2+7^3\right)+\left(7^4+7^5\right)+...+\left(7^{100}+7^{101}\right)\)

\(B=8+7^2\left(1+7\right)+7^4\left(1+7\right)+...+7^{100}\left(1+7\right)\)

\(B=8+7^2\cdot8+7^4\cdot8+...+7^{100}\cdot8\)

\(B=8\left(1+7^2+7^4+...+7^{100}\right)\)

\(\text{Vì 8⋮8}\Rightarrow8\left(1+7^2+7^4+...+7^{100}\right)⋮8\)

\(\text{Hay B⋮8}\)

\(\text{Vậy B⋮8}\)

Answer 2

\(B=1+7+7^2+7^3+7^4+...+7^{101}\)

\(B=\left(1+7\right)+\left(7^2+7^3\right)+\left(7^4+7^5\right)+...+\left(7^{100}+7^{101}\right)\)

\(B=8+7^2\left(1+7\right)+7^4\left(1+7\right)+...+7^{100}\left(1+7\right)\)

\(B=8+7^2\cdot8+7^4\cdot8+...+7^{100}\cdot8\)

Answer 3

B = (1+7) + (7²+7³) + (7⁴+7⁵)+...+(7¹⁰⁰+7¹⁰¹)

B = 1 x (1+7)+ 7²x (1+7) + 7⁴x(1+7) +...+ 7¹⁰⁰x (1+7)

B = (1+7²+7⁴+...+7¹⁰⁰) x (1+7)

B = ( 1+7²+7⁴+...+7¹⁰⁰) x 8

Vì 8 chia hết cho 8 nên (1+7² +7⁴+...+7¹⁰⁰) x 8 chia hết cho 8 

Vậy B chia hết cho 8

Study well !

Answer 4

\(B=1+7+7^2+7^3+7^4+...+7^{101}\)

\(B=\left(1+7\right)+\left(7^2+7^3\right)+\left(7^4+7^5\right)+...+\left(7^{100}+7^{101}\right)\)

\(B=8+7^2\left(1+7\right)+7^4\left(1+7\right)+...+7^{100}\left(1+7\right)\)

\(B=8+7^2\cdot8+7^4\cdot8+...+7^{100}\cdot8\)

Answer 5

\(B=1+7+7^2+7^3+7^4+...+7^{101}\)

\(\Rightarrow B=\left(1+7\right)+\left(7^2+7^3\right)+\left(7^4+7^5\right)+...+\left(7^{100}+7^{101}\right)\)

\(\Rightarrow B=8+7^2.\left(1+7\right)+7^4.\left(1+7\right)+...+7^{100}.\left(1+7\right)\)

\(\Rightarrow B=8.1+7^2.8+7^4.8+...+7^{100}.8\)

\(\Rightarrow B=\left(1+7^2+7^4+...+7^{100}\right).8\)

Vì \(8⋮8\)nên \(\left(1+7^2+7^4+...+7^{100}\right).8⋮8\)

hay \(B⋮8\)

Answer 6

Các bạn giải thích hộ mình với

Answer 7

Sao đằng sau ra được 1+7 vậy

Answer 8

B= 1 + 7 + 7^2 + 7^3 +7^4+.............7^101

B= (1 + 7 ) +(7^2+7^3)+(7^4=7^50+)............+(7^100+7^101)

B=8 + 7^2(1+7)+7^4+.............+7^100 + ( 1+7)

B= 8 +7^2.8+7^4+7^4+8+7^100

Answer 9

đặt số chung ra ngoài thì đc 1+7

Answer 10

B=1+7+7²+7³+7⁴...+7¹⁰¹ =(1+7)+(7²+7³)+....+(7¹⁰⁰+7¹⁰¹) =8+7².(1+7)+...+7¹⁰⁰.(1+7) =8+7².8+....+7¹⁰⁰.8 =8.(1+7²+...+7¹⁰⁰) Suy ra B chia hết cho 8