\(A=1+5+5^2+5^3+...+5^{59}\)

\(=\left(1+5+5^2\right)+\left(5^3+5^4+5^5\right)+...+\left(5^{57}+5^{58}+5^{59}\right)\)

\(=\left(1+5+5^2\right)+5^3\left(1+5+5^2\right)+...+5^{57}\left(1+5+5^2\right)\)

\(=31\left(1+5^3+...+5^{57}\right)\)chia hết cho \(31\).

\(A=1+5+5^2+5^3+...+5^{59}\)

\(5A=5+5^2+5^3+5^4+...+5^{60}\)

\(5A-A=\left(5+5^2+5^3+5^4+...+5^{60}\right)-\left(1+5+5^2+5^3+...+5^{59}\right)\)

\(4A=5^{60}-1\)

\(A=\frac{5^{60}-1}{4}< \frac{5^{60}}{4}\).

Cho hình vẽ bạn ơi 

đợi mik tí

\(-2x=5.\left(-5\right)+3\)

\(\Rightarrow-2x=-25+3\)

\(\Rightarrow-2x=-22\)

\(\Rightarrow x=11\)

Vậy: \(x=11\)

\(\left(-17\right).75+\left(-25\right).17-120\)

\(=-17.\left(75+25\right)-120\)

\(=-17.100-120\)

\(=-1700-120\)

\(=-1820\)

\(\left[\left(14-38\right):2-4\right].\left(-2\right)\)

\(=\left(-24:2-4\right).\left(-2\right)\)

\(=\left(-12-4\right).\left(-2\right)\)

\(=-16.\left(-2\right)\)

\(=32\)

TL:

=[(14-38):2-4].(-2)

=[(-24) : (-2)].(-2)

=(-12).(-2)

=(-24)

Học Tốt 👍

\(123-4\left(x-2\right)^2=23\)

\(\Rightarrow-4\left(x-2\right)^2=-100\)

\(\Rightarrow\left(x-2\right)^2=25\)

\(\Rightarrow\orbr{\begin{cases}x-2=5\\x-2=-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=7\\x=-3\end{cases}}\)

Vậy: \(x\in\left\{7;-3\right\}\)

( -17 ) . 75 + (-25 ). 17 – 120

=17.(-1).75+(-25).17-120

=17.(-75-25)-120

=17.(-100)-120

=-1700-120

=-1820

  65 . (- 45 ) – 35. 45 + 24 .( -21 )+ 76.( -21 )

=65.(-1).45-35.45+24.(-21)+76.(-21)

=45.(-65-35)+(-21).(24+76)

=45.(-100)+(-21).100

=-4500-2100

=-6600

65 . (- 45 ) – 35. 45 + 24 .( -21 )+ 76.( -21 )

= ( 65 + 35 ) . ( 76 + 24 ) . ( -21) - (-21) . ( 45 + (-45)

= 100 . 100 . 0 .0

= cuối cùng thì đều bằng 0