1) \(B=1+5+5^2+5^3+....+5^{101}\)
\(=\left(1+5\right)+\left(5^2+5^3\right)+.....+\left(5^{100}+5^{101}\right)\)
\(=\left(1+5\right)+5^2\left(1+5\right)+....+5^{100}\left(1+5\right)\)
\(=\left(1+5\right)\left(1+5^2+....+5^{100}\right)\)
\(=6\left(1+5^2+...+5^{100}\right)\)\(⋮6\)
2) \(C=81^3+3^{14}+27^5\)
\(=\left(3^4\right)^3+3^{14}+\left(3^3\right)^5\)
\(=3^{12}+3^{14}+3^{15}\)
\(=3^{12}.\left(1+3^2+3^3\right)\)
\(=3^{12}.37\)\(⋮37\)
3) \(D=2+2^2+2^3+...+2^{60}\)
\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+....+2^{59}\left(1+2\right)\)
\(=\left(1+2\right)\left(2+2^3+...+2^{59}\right)\)
\(=3\left(2+2^3+...+2^{59}\right)\)\(⋮3\)
chứng minh chia hết cho 7, 15 bạn làm tương tự
chia hết cho 7: bạn nhóm 3 số thành nhóm
chia hết cho 15: bạn nhóm 4 số thành nhóm