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Thôi chịu 

52 phân tích ra được là 1 + 17.3 =))

1)

a) $A=3+3^2+3^3+3^4+3^5+3^6+....+3^{28}+3^{29}+3^{30}$

$\iff A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+....+\left(3^{28}+3^{29}+3^{30}\right)$

$\iff A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+....+3^{28}\left(1+3+3^2\right)$

$\iff A=3.13+3^4.13+....+3^{28}.13$

$\iff A=13\left(3+3^4+....+3^{28}\right)⋮13\left(dpcm\right)$

b) $A=3+3^2+3^3+3^4+3^5+3^6+....+3^{25}+3^{26}+3^{27}+3^{28}+3^{29}+3^{30}$

$\iff A=\left(3+3^2+3^3+3^4+3^5+3^6\right)+....+\left(3^{25}+3^{26}+3^{27}+3^{28}+3^{29}+3^{30}\right)$

$\iff A=3\left(1+3+3^2+3^3+3^4+3^5\right)+....+3^{25}\left(1+3+3^2+3^3+3^4+3^5\right)$

$\iff A=3.364+....+3^{25}.364$

$\iff A=364\left(3+3^5+3^{10}+....+3^{25}\right)$

$\iff A=52.7\left(3+3^5+3^{10}+....+3^{25}\right)⋮52\left(dpcm\right)$

2) $A=3+3^2+3^3+....+3^{30}$

$\iff 3A=3\left(3+3^2+3^3+....+3^{30}\right)$

$\iff 3A=3^2+3^3+3^4+....+3^{30}+3^{31}$

$\iff 3A-A=\left(3^2+3^3+3^4+....+3^{30}+3^{31}\right)-\left(3+3^2+3^3+....+3^{30}\right)$

$\iff 2A=3^{31}-3$

⇔A=331−32⇔�=331−32

Vậy A không phải là số chính phương
Học tốt nha

cố gắng làm nhanh cho mk nha!!!

mk cảm mơn nhiều 

b, \(B=5+5^2+5^3+5^4+...+5^{11}+5^{12}\)

\(B=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{11}+5^{12}\right)\)

\(B=30+5^2\left(5+5^2\right)+...+5^{10}\left(5+5^2\right)\)

\(B=30+5^2\cdot30+...+5^{10}\cdot30\)

\(B=\left(1+5^2+...+5^{10}\right)\cdot30\)\(⋮30\)

+) \(B=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+...+\left(5^{10}+5^{11}+5^{12}\right)\)

\(B=5\left(1+5+5^2\right)+5^4\left(1+5+5^2\right)+...+5^{10}\left(1+5+5^2\right)\)

\(B=5\cdot31+5^4\cdot31+...+5^{10}\cdot31\)

\(B=\left(5+5^4+...+5^{10}\right)\cdot31\)\(⋮31\)

a,964 865, 766, 973,...

b,1

c,1152

d,3645

\(A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+...+3^{2008}\left(1+3+3^2\right)\)

\(=13\cdot\left(3+3^4+...+3^{2008}\right)\)

\(=13\cdot\left[3\left(1+3^3\right)+...+3^{2005}\left(1+3^3\right)\right]\)

\(=13\cdot4\cdot7\cdot\left(3+...+3^{2005}\right)⋮52\)

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