Question

1.1/2+1.2/3+1/3.4+1/4.5+..+1/x(x+1)=499/500

Answer 1

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow x=499\)

Answer 2

giúp e vs

 

 

Answer 3

 

Answer 4

Nên gõ latex , với cả  không theo quy luật.

Answer 5

Ta có: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow x=499\)