\(B=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+...+\dfrac{4}{125\times129}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{125}-\dfrac{1}{129}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{129}\right)=\dfrac{1}{4}\times\dfrac{128}{129}=\dfrac{32}{129}\)

\(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+...+\dfrac{1}{45\times49}\)

\(=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{45\times49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{45}-\dfrac{1}{49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{49}\right)=\dfrac{1}{4}\times\dfrac{48}{49}=\dfrac{12}{49}\)

A = 3/1×5 + 3/5×9 + 1/9×13 + ... + 9/97×101 + 3/101×105

A = 3/4 × (4/1×5 + 4/5×9 + 4/9×13 + ... + 4/97×101 + 4/101×105)

A = 3/4 × (1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/97 - 1/101 + 1/101 - 1/105)

A = 3/4 × (1 - 1/105)

A = 3/4 × 104/105

A = 26/35

B = 1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625

5B = 1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125

5B - B = (1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125) - (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)

4B = 1 - 1/15625

4B = 15624/15625

B = 15624/15625 : 4

B = 3906/15625

C = 1 + 2 + 4 + 8 + 16 + ... + 2048 + 4096

2C = 2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192

2C - C = (2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192) - (1 + 2 + 4 + 8 + ... + 2048 + 4096)

B = 8192 - 1

B = 8191

Soyeon_Tiểu Bàng Giải lm đúng òi

A = 3/1×5 + 3/5×9 + 1/9×13 + ... + 9/97×101 + 3/101×105

A = 3/4 × (4/1×5 + 4/5×9 + 4/9×13 + ... + 4/97×101 + 4/101×105)

A = 3/4 × (1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/97 - 1/101 + 1/101 - 1/105)

A = 3/4 × (1 - 1/105)

A = 3/4 × 104/105

A = 26/35

B = 1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625

5B = 1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125

5B - B = (1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125) - (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)

4B = 1 - 1/15625

4B = 15624/15625

B = 15624/15625 : 4

B = 3906/15625

C = 1 + 2 + 4 + 8 + 16 + ... + 2048 + 4096

2C = 2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192

2C - C = (2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192) - (1 + 2 + 4 + 8 + ... + 2048 + 4096)

B = 8192 - 1

B = 8191

\(\left(2007-2005\right)+\left(2003-2001\right)+...+\left(7-5\right)+\left(3-1\right)\)

\(=2+2+...+2\)

\(=2.1004=2008\)

\(\dfrac{1}{1.5};\dfrac{1}{5.9};\dfrac{1}{9.13};\dfrac{1}{13.17}\)

a) \(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{47.49}=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+......+\frac{2}{47.49}\right)=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{47}-\frac{1}{49}\right)=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\left(1-\frac{1}{49}\right)=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\frac{48}{49}=\frac{24}{x+4}\)

\(\Rightarrow\frac{24}{49}=\frac{24}{x+4}\)

\(\Rightarrow x+4=49\Rightarrow x=45\)

\(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{47.49}=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{47.49}\right)=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{47}-\frac{1}{49}\right)=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{49}\right)=\frac{24}{x+4}\Leftrightarrow A=\frac{1}{2}.\frac{48}{49}=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{24}{49}=\frac{24}{x+4}\Leftrightarrow x=49-4=45\)

Bài b) hình như sai đề thì phải đó bạn.

a)ta co \(\frac{1}{1.3}+\frac{1}{3.5}+..+\frac{1}{47.49}=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{47}-\frac{1}{49}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{49}\right)=\frac{24}{49}=\frac{24}{x+4}\)\(\Rightarrow49=x=4\Rightarrow x=45\)

b)ta co \(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{97.101}=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}=\frac{2x+4}{101}\Rightarrow100=2x+4\Rightarrow x=48\)

A = 4/1 x 5 + 4/5 x 9 + 4/9 x 13 + .... + 4/91 x 95 + 4/95 x 99

A = 1 - 1/5 + 1/5 -1/9 + 1/9 - 1/13 + .... + 1/91 - 1/95 + 1/95 - 1/99

A = 1 - 1/99

A = 98/99

B = 1/6 + 1/12 + 1/20 + ... + 1/132

B = 1/2 x 3 + 1/3 x 4 + 1/4 x 5 + ... + 1/11 x 12

B = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/11 - 1/12 

B = 1/2 - 1/12 

B = 5/12