Ta có :

\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+....+\frac{1}{\left(x+5\right)\left(x+6\right)}\)

\(=\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+....+\frac{1}{x+5}-\frac{1}{x+6}\)

\(=\frac{1}{x}-\frac{1}{x+6}\)

\(=\frac{6}{x\left(x+6\right)}\)

 -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

S = 1 * 2 + 2 * 3 + 3 * 4 + ...... + 28 * 29 + 29 * 30

3S = 1 x 2 x 3 - 1 x 2 x 3 + 2 x 3 x 4 - 2 x 3 x 4 + .............. + 29 x 30 x 31

3S = 29 x 30 x 31

S = 29 x 30 x 31 : 3 = 8990

Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 28.29 + 29.30

<=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 29.30.31

<=> 3S = 29.30.31 

<=> S = 29.30.31 / 3 = 8990

Chúc học tốt nhé !

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

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

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

\(3x=-21\)

\(x=-7\)