*T.
\(T=3+3^2+3^3+...+3^9\)
\(T=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+\left(3^7+3^8+3^9\right)\)
\(T=3\left(1+3+3^2\right)+3^4\left(1+3^2+3^3\right)+3^7\left(1+3^2+3^3\right)\)
\(T=\left(1+3+3^2\right)\left(3+3^4+3^7\right)\)
\(T=13\left(3+3^4+3^7\right)⋮13\)
*P.
\(P=1+2+2^2+2^3+...+2^7\)
\(P=\left(1+2\right)+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)
\(P=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)
\(P=\left(1+2\right)\left(2^2+2^4+2^6\right)\)
\(P=3\left(2^2+2^4+2^6\right)⋮3\)
Câu A để coi lại -.-
T = 3 + 32 + 33 + ... + 39
\(\Rightarrow\) 3T = 32 + 33 + 34 + ... + 310
\(\Rightarrow\) 3T - T = (32 + 33 + 34 + ... + 310) - (3 + 32 + 33 + ... + 39)
\(\Rightarrow\) 2T = 310 - 3
= 59049 - 3 = 59046
\(\Rightarrow\) T = 29523
Vì 29523 \(⋮\) 13 nên T \(⋮\) 13
\(\Rightarrow\) ĐPCM
A = 1 + 2 + 22 + ... + 211
\(\Rightarrow\) 2A = 2 + 22 + 23 + ... + 212
\(\Rightarrow\) 2A - A = (2 + 22 + 23 + ... + 212) - (1 + 2 + 22 + ... + 211)
\(\Rightarrow\) A = 212 - 1
= 4096 - 1 = 4095
Vì 4095 \(⋮\) 9 nên A \(⋮\) 9
\(\Rightarrow\) ĐPCM
