A=(13+13²)+(13³+13⁴)+.......................+(13⁹⁹+13¹⁰⁰)

A=1.(13+13²)+13².(13+13²)+..............+13⁹⁸.(13+13²)

A=1.182+13².182+..........................+13⁹⁸.182

A+182.(1+13²+..............+13⁹⁸) Chia hết cho 182

--> A chia hết cho 182

Ta có: \(A=\left(13+13^2\right)+\left(13^3+13^4\right)+\left(13^5+13^6\right)\)

                \(=13\left(13+1\right)+13^3\left(13+1\right)+13^5\left(13+1\right)\)

                \(=14\left(13+13^3+13^5\right)\)

                 \(=2.7.\left(13+13^3+13^5\right)\) chia hết cho 2

phạm ngọc thạch sai 35% 

Xin lỗi mk viết nhầm 

12A=13¹⁰¹-1

=>\(A=\frac{13^{101}-1}{12}\)

(13¹⁰¹-13):12

chich di

\(ta có A=\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{15}}{13^{16}}+1\)=\(\dfrac{1}{13}+1\)

B=\(\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{16}}{13^{17}}+1\)=\(\dfrac{1}{13}+1\)

vậy A=B

\(A=\dfrac{13^{15}+1}{13^{16}+1}vàB=\dfrac{13^{16}+1}{13^{17}+1}\)

ta có

\(\dfrac{13^{16}+1}{13^{17}+1}< 1\Rightarrow\dfrac{13^{16}+1+12}{13^{17}+1+12}=\dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\dfrac{13^{15}+1}{13^{16}+1}=A\)

vậy B<A

\(A=\dfrac{13^{15}+1}{13^{16}+1}vàB=\dfrac{13^{16}+1}{13^{17}+1}\)

ta có B<1 nên

\(\dfrac{13^{16}+1}{13^{17}+1}< \dfrac{13^{16}+1+12}{13^{17}+1+12}=\dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\dfrac{13^{15}+1}{13^{16}+1}=A\)

Vậy B<A

nhân 13 với A và B

so sánh mẫu =>mẫu nào lớn hơn thì bé hơn

là xong

`2/13 . 5/9+ 2/13 . 4/9 +11/13`

`= 2/13 . ( 5/9 + 4/9)+11/13`

`= 2/13 . 9/9 +11/13`

`= 2/13 . 1 + 11/13`

`= 2/13 +11/13`

`=13/13`

`=1`

`@ yl`

`2/13*5/9+2/13*4/9+11/13`

`=2/13*(5/9+4/9)+11/13`

`=2/13*9/9+11/13`

`=2/13*1+11/13`

`=2/13+11/13`

`=13/13=1`

\(A=\dfrac{2}{13}\times\dfrac{5}{9}+\dfrac{2}{13}\times\dfrac{4}{9}+\dfrac{11}{13}\\ A=\dfrac{2}{13}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{11}{13}\\ A=\dfrac{2}{13}\times1+\dfrac{11}{13}\\ A=\dfrac{2}{13}+\dfrac{11}{13}\\ A=1\)