Question

Bài 8: Chứng tỏ rằng:

a) 7^0 + 7^1 + 7^2 + 7^3 + ....... + 7^2010 + 7^2011 chia hết cho 8

Giup mình bài này với!

Answer 1

\(7^0+7^1+7^2+7^3+....+7^{2010}+7^{2011}\)

\(=\left(1+7\right)+\left(7^2+7^3\right)+....+\left(7^{2010}+7^{2011}\right)\)

\(=\left(1+7\right)+7^2\left(1+7\right)+....+7^{2010}\left(1+7\right)\)

\(=8+7^2.8+....+7^{2010}.8\)

\(=8\left(1+7^2+....+7^{2010}\right)⋮8\left(dpcm\right)\)