Câu hỏi của Linh Hoàng

Question

Bài 1: Chứng minh rằng với mọi số tự nhiên n thì:
b, F= 9^2n+1 +1 chia hết cho 10

c, H= 7^4n - 1 chia hết cho 5

Phạm Trần Hoàng Anh · Accepted Answer

b) $9^{2n+1}+1=\left(9^2\right)^n.9+1=81^n.9+1=\overline{...1}.9+1=\overline{...9}+1=\overline{...0}⋮10$

c)

$7^{4n}-1=\left(7^4\right)^n-1=2401^n-1=\overline{...1}-1=\overline{...0}⋮5$

Câu trả lời:

b) $9^{2n+1}+1=\left(9^2\right)^n.9+1=81^n.9+1=\overline{...1}.9+1=\overline{...9}+1=\overline{...0}⋮10$

c)

$7^{4n}-1=\left(7^4\right)^n-1=2401^n-1=\overline{...1}-1=\overline{...0}⋮5$

HT.Phong (9A5) · Answer

b) `F=9^(2n+1)+1=9^(2n)*9+1`

Ta có:

$9^{2n}=\overline{...1}=>9\cdot9^{2n}=9^{2n+1}=\overline{...9}\ =>F=9^{2n+1}+1=\overline{...9}+1=\overline{...0}⋮10$

c) `H=7^(4n)-1`

Ta có:

$7^{4n}=\overline{....1}=>H=7^{4n}-1=\overline{...1}-1=\overline{...0}⋮10$

Câu trả lời:

b) `F=9^(2n+1)+1=9^(2n)*9+1`

Ta có:

$9^{2n}=\overline{...1}=>9\cdot9^{2n}=9^{2n+1}=\overline{...9}\ =>F=9^{2n+1}+1=\overline{...9}+1=\overline{...0}⋮10$

c) `H=7^(4n)-1`

Ta có:

$7^{4n}=\overline{....1}=>H=7^{4n}-1=\overline{...1}-1=\overline{...0}⋮10$