Question

[Minhchau Trần]

2021/1.5 + 2021/5.9 + 2021/9.14 +....+ 2021/x.(x+4) = 505

giúp mk vs. TKS mn

Answer 1

[Nguyễn Đình Nhật Long]

\(\dfrac{2021}{1\cdot5}+\dfrac{2021}{5\cdot9}+...+\dfrac{2021}{x\cdot\left(x+4\right)}=505\)

\(2021\cdot\left(\dfrac{1}{1.5}+\dfrac{1}{5\cdot9}+...+\dfrac{1}{x\cdot\left(x+4\right)}\right)=505\)

\(\dfrac{2021}{4}\cdot\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{x\cdot\left(x+4\right)}\right)=505\)

\(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(1-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(\dfrac{1}{x+4}=\dfrac{1}{2021}\)

=> \(x+4=2021\)

=> \(x=2017\)

vậy \(x=2017\)

Answer 2

[Nguyễn Lê Phước Thịnh]

Ta có: \(\dfrac{2021}{1\cdot5}+\dfrac{2021}{5\cdot9}+...+\dfrac{2021}{x\left(x+4\right)}=505\)

\(\Leftrightarrow\dfrac{2021}{4}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{x\left(x+4\right)}\right)=505\)

\(\Leftrightarrow1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(\Leftrightarrow-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(\Leftrightarrow x+4=\dfrac{-2021}{2020}\)

hay \(x=-\dfrac{10101}{2020}\)