1/3x4 + 1/4x5 + 1/5x6 +...+ 1/97x 98 + 1/98x99 + x =1

=> 1/3-1/4+1/4-1/5+1/5-1/6+....+1/97-1/98 + 1/98-1/99 +x = 1

=> 1/3 - 1/99 +x=1

=>  32/99+x=1

=> x= 1-32/99

=> x = 67/99

67/99

\(\left(x+\dfrac{1}{2\times3}\right)+\left(x+\dfrac{1}{3\times4}\right)+\left(x+\dfrac{1}{4\times5}\right)+\left(x+\dfrac{1}{5\times6}\right)=\dfrac{25}{3}\)

\(x+\dfrac{1}{2\times3}+x+\dfrac{1}{3\times4}+x+\dfrac{1}{4\times5}+x+\dfrac{1}{5\times6}=\dfrac{25}{3}\)

\(x\times4+\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}\right)=\dfrac{25}{3}\)

\(x\times4+\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\right)=\dfrac{25}{3}\)

\(x\times4+\left(\dfrac{1}{2}-\dfrac{1}{6}\right)=\dfrac{25}{3}\)

\(x\times4+\dfrac{4}{12}=\dfrac{25}{3}\)

\(x\times4=\dfrac{25}{3}-\dfrac{4}{12}\)

\(x\times4=\dfrac{25}{3}-\dfrac{1}{3}\)

\(x\times4=\dfrac{24}{3}\)

\(x\times4=8\)

\(x=8\div4\)

\(x=2\)

:))

=1/2-1/3+1/3-1/4+.......+1/a-1/a+1=49/100

1/2-1/a+1=49/100

1/a+1 = 1/2-49/100

1/a+1=1/100

a+1=100

a=99

=1/2-1/3+1/3-1/4+.......+1/a-1/a+1=49/100

1/2-1/a+1=49/100

1/a+1 = 1/2-49/100

1/a+1=1/100

a+1=100

a=99

\(\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2008}{2010}\\ 2\cdot\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2008}{2010}\\ \dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2008}{2010}:2\\ \dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{1004}{2010}\\ \dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{1004}{2010}\\ \dfrac{1}{x+1}=\dfrac{1}{2010}\\ \Rightarrow x+1=2010\\ \Rightarrow x=2009\)

nhìn đề bài ko hỉu j hết

\(\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2008}{2010}\)

\(\Rightarrow2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2008}{2010}\)

\(\Rightarrow\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{502}{1005}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{502}{1005}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{502}{1005}\)

\(\Rightarrow\dfrac{1}{x+1}=\dfrac{1}{2010}\)

\(\Rightarrow x+1=2010\Rightarrow x=2009\)

Ta có:

Suy ra đa thức Q(x) có bậc là 5

Chọn đáp án B

\(P=\left(1-\frac{2}{2.3}\right).\left(1-\frac{2}{3.4}\right).\left(1-\frac{2}{4.5}\right)...\left(1-\frac{2}{99.100}\right)\)

\(P=\frac{4}{2.3}.\frac{10}{3.4}.\frac{18}{4.5}...\frac{9898}{99.100}\)

\(P=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{98.101}{99.100}\)

\(P=\frac{1.2.3...98}{2.3.4...99}.\frac{4.5.6...101}{3.4.5...100}\)

\(P=\frac{1}{99}.\frac{101}{3}=\frac{101}{297}\)

Bài nào khó lắm thì mới hỏi thôi chứ bài này dễ mà bạn tự vận động não đi

\(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{11\cdot12}=x\)

\(\Leftrightarrow x=\dfrac{1}{3}-\dfrac{1}{12}=\dfrac{4}{12}-\dfrac{1}{12}=\dfrac{1}{4}\)

dễ lắm ko cần hỏi đâu ,tự vận động não đi

\(B=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2022.2023}\)

\(B=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\)

\(B=\dfrac{1}{2}-\dfrac{1}{2023}=\dfrac{2021}{4046}\)

\(\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{20\times21}=\dfrac{x}{14}\)

\(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{20}-\dfrac{1}{21}=\dfrac{x}{14}\)

\(\dfrac{1}{3}-\dfrac{1}{21}=\dfrac{x}{14}\)

\(\dfrac{7}{21}-\dfrac{1}{21}=\dfrac{x}{14}\)

\(\dfrac{6}{21}=\dfrac{x}{14}\)

\(\Rightarrow x.21=6.14\)

\(x.21=84\)

\(x=84:21\)

\(x=4\)

Vậy x = 4

1/3x4 + 1/4x5 + 1/5x6 + .. + 1/20x21 = x/14

1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + .. + 1/20 - 1/21 = x/14

1/3 - 1/21 = x/14

7/21 - 1/21 = x/14

6/21 = x/14

x . 21 = 6 x 14

x x 21 = 84

x = 84 : 21

x = 4

1/(3×4) + 1/(4×5) + 1/(5×6) + ... + 1/(20×21) = x/14

1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/20 - 1/21 = x/14

1/3 - 1/21 = x/14

2/7 = x/14

x = 14 × 2/7

x = 4