Question

Tìm x,biết: \(\dfrac{1}{15}\)+\(\dfrac{1}{21}\)+\(\dfrac{1}{28}\)+\(\dfrac{1}{36}\)+...+\(\dfrac{2}{x\left(x+1\right)}\)=\(\dfrac{11}{40}\) (x thuộc N*)

giúp mik vs ạ mik đg cần gấp ạ

Answer 1

\(\Leftrightarrow2\left(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{11}{40}\)

=>1/5-1/x+1=11/80

=>1/x+1=5/80=1/16

=>x=15

Answer 2

\(\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{11}{40}\)

\(\Rightarrow2\left(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{11}{40}\)

\(\Rightarrow2\left(\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{11}{40}\)

\(\Rightarrow2\left(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{11}{40}\)

\(\Rightarrow\dfrac{1}{5}-\dfrac{1}{x+1}=\dfrac{11}{80}\Rightarrow x=15\)

 

Answer 3

`[50]`

`2/30 + 2/42 + ... + 2/(x(x+1)) = 11/40`

`2/(5.6) + 2/(6.7) + ... + 2/(x(x+1)) = 11/40`

`-> 1/2 . (1/5 - 1/6 +1/6 - 1/7 + 1/x - 1/(x+1)) = 11/40`

`-> 1/5 - 1/(x+1) = 11/40`

`-> x = 15`