-29.(85-47)-85.(47-29)

=-29.38-85.18

=-1102-1503

=-2605

-15.(23-29)+23-(15-29)

=-15.(-6)+23-(-14)

=90+23+14

=113+14

=127

 -13.(55-29)+23.(15-29)

=-13.26+23.(-14)

=-338+(-322)

=-660

-10.(2+4)-5.(4-3)

=-10.6-5.1

=-60-5

=-65

Ta có \(\left(29^m+1\right)\left(29^m+2\right)\left(29^m+3\right)\left(29^m+4\right)\)

 \(\Rightarrow29^m\left(1+2+3+4\right)=29^m\cdot10⋮5\)

= 29 ^m +1 x 29^m+2 x 29^m+3 x 29^m+4

= 29^m x (1+2+3+4)

=29^mx10 chia hết cho 5

=> 29^m + 1 x 29^m + 2 x 29^m + 3 x 29^m + 4 chia hết cho 5

\(\left(5x-29\right)-\left(2x-29\right)=-21\)

\(5x-29-2x+29=-21\)

\(5x-2x=-21+29-29\)

\(3x=-21\)

\(x=-7\)

\(=4+\dfrac{5}{58}-3-\dfrac{1}{2}+8+\dfrac{15}{29}-3-\dfrac{5}{58}+7+\dfrac{14}{29}=13+\dfrac{1}{2}=\dfrac{27}{2}\)

\(1,-\frac{3}{29}+\frac{-7}{29}\le\frac{x}{29}\le-\frac{3}{29}-\frac{5}{29}\)

\(\Rightarrow-\frac{10}{29}\le\frac{x}{29}\le-\frac{8}{29}\Rightarrow-10\le x\le-8\)

\(\Rightarrow x=\left\{-8;-9;-10\right\}\)

\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)

\(\Rightarrow2S=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\)

             \(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)

\(\Rightarrow2S-S=S=1-\frac{1}{2^{100}}\)