\(B=7+7^2+...+7^{100}\)
\(B=\left(7+7^2\right)+...+\left(7^{99}+7^{100}\right)\)
\(B=7\left(1+7\right)+...+7^{99}\left(1+7\right)\)
\(B=7\cdot8+...+7^{99}\cdot8\)
\(B=8\cdot\left(7+...+7^{99}\right)⋮8\left(đpcm\right)\)
\(B=7+7^2+7^3+...+7^{100}\)
\(B=\left(7+7^2+7^3\right)+...+\left(7^{98}+7^{99}+7^{100}\right)\)
\(B=399\cdot1+...+7^{97}\cdot\left(7+7^2+7^3\right)\)
\(B=399\cdot1+...+7^{97}\cdot399\)
\(B=399\cdot\left(1+...+7^{97}\right)⋮399\left(đpcm\right)\)
\(B=7+7^2+7^3+7^4+7^5+7^6+....+7^{100}\)
\(=\left(7+7^2\right)+\left(7^3+7^4\right)+...+\left(7^{99}+7^{100}\right)\)
\(=7.\left(1+7\right)+7^3.\left(1+7\right)+...+7^{99}.\left(1+7\right)\)
\(=7.8+7^3.8+...+7^{99}.8\)
\(=8.\left(7+7^3+...+7^{99}\right)⋮8\)
Vậy B chia hết cho 8
Ta lại có: \(B=\left(7+7^2+7^3\right)+\left(7^4+7^5+7^6\right)+...+\left(7^{98}+7^{99}+7^{100}\right)\)
\(=\left(7+7^2+7^3\right)+7^3.\left(7+7^2+7^3\right)+....+7^{97}.\left(7+7^2+7^3\right)\)
\(=399+7^3.399+.....+7^{97}.399\)
\(=399.\left(1+7^3+....+7^{97}\right)⋮399\)
Vậy B chia hết cho 399
B = (7+7^2) + (7^3+7^4) +...+ (7^99+7^100)
B = 7.(7+1) + 7^3.(7+1) +...+ 7^99.(7+1)
B = 7.8 + 7^3.8 +...+ 7^99.8
B = 8.(7+7^3+...+7^99) chia hết cho 8
Vậy B chia hết cho 8
B = (7+7^2+7^3) +...+ (7^98+7^99+7^100)
B = 7.(7+7^2+7^3) +...+ 7^98.(7+7^2+7^3)
B = 7.399 +...+ 7^98.399
B = 399.(7+...+7^98) chia hết cho 399
Vậy B chia hết cho 399
*) \(B=7+7^2+7^3+...+7^{100}\)
\(\Rightarrow B=\left(7+7^2\right)+\left(7^3+7^4\right)+...+\left(7^{99}+7^{100}\right)\)
\(\Rightarrow B=7\left(1+7\right)+7^3\left(1+7\right)+...+7^{99}\left(1+7\right)\)
\(\Rightarrow B=7\cdot8+7^3\cdot8+...+7^{99}\cdot8\)
\(\Rightarrow B=8\left(7+7^3+...+7^{99}\right)\)
\(\Rightarrow B⋮8\left(đpcm\right)\)
*) \(B=7+7^2+7^3+...+7^{100}\)
\(\Rightarrow B=\left(7+7^2+7^3\right)+\left(7^4+7^5+7^6\right)+...+\left(7^{98}+7^{99}+7^{100}\right)\)
\(\Rightarrow B=399+7^3\left(7+7^2+7^3\right)+...+7^{97}\left(7+7^2+7^3\right)\)
\(\Rightarrow B=399+7^3\cdot399+...+7^{97}\cdot399\)
\(\Rightarrow B=399\left(1+7^3+...+7^{97}\right)\)
\(\Rightarrow B⋮399\left(đpcm\right)\)
