Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{x\left(x+1\right):2}=\frac{399}{400}\)

\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.....+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\left(\text{​Quy đồng nhé !}\right)\)

\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+......+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)

\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{x\left(x+1\right)}\right)=\frac{399}{400}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+.....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{399}{400}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{399}{400}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{800}\)

=> x + 1 = 800 

<=> x = 799

1/3+1/6+1/10+...+1/x(x+1):2=399/400

2.[1/3.2+1/6.2+1/10.2+...+1/x(x+1)]=399/400

2.[1/6+1/12+1/20+...+1/x(x+1)]=399/400

2.[1/2.3+1/3.4+1/4.5+...+1/x(x+1)]=399/400

1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=399/800

1/2-1/x+1=399/800

1/x+1=1/800

=> x+1=800

=> x=799

4

9,5 x X = 399

X = 399 : 9,5

X = 42

9,5 x x = 399

x = 399 : 9,5

x = 42

Bài 1 :

a) \(a.b+b.19=713\) \(\left(a;b\inℕ^∗\right)\)

\(\Rightarrow b.\left(a+19\right)=713\)

\(\Rightarrow\left(a+19\right);b\in\left\{1;23;31;713\right\}\)

\(\Rightarrow\left(a;b\right)\in\left\{\left(-18;713\right);\left(4;31\right);\left(12;23\right);\left(694;1\right)\right\}\)

\(\Rightarrow\left(a;b\right)\in\left\{\left(4;31\right);\left(12;23\right);\left(694;1\right)\right\}\left(a;b\inℕ^∗\right)\)

b) \(a.b-10.b=650\)

\(\Rightarrow b.\left(a-10\right)=650\)

\(\Rightarrow\left(a-10\right);b\in\left\{1;5;10;13;25;26;50;65;130;325;650\right\}\)

Bạn lập bảng sẽ tìm ra (a;b)...

Bài 2 :

a) \(3^4+3^5+3^6+3^7=3^4\left(1+3+3^2+3^3\right)=3^4.40\)

b) \(B=1+3+3^2+3^3+...+3^{99}\)

\(\Rightarrow B=\left(1+3+3^2+3^3\right)+3^4.\left(1+3+3^2+3^3\right)...+3^{96}.\left(1+3+3^2+3^3\right)\)

\(\Rightarrow B=40+3^4.40...+3^{96}.40\)

\(\Rightarrow B=40\left(1+3^4...+3^{96}\right)⋮40\)

\(\Rightarrow dpcm\)

a) X = 11                           b) X = 2020 

`4,32+x=8,67`

`x=8,67-4,32`

`x=4,35`

___________________________

\(9,5\times x=399\)

`x=399:9,5`

`x=42`

Nhanh lên được ko a

Tồng của 3 số là:

457x3=1371

Tổng của số thứ 1 và số thứ 2 là:

399x2=798

Số thứ 3 là:

1371-798=573

      Đáp số: 573