Question

[Đặng Ngọc Anh]

tìm X: 3 x [1/5x8 + 1/8x11 + 1/11x14 + ... + 1/97x100 + X] = 319/100

Answer 1

[Xyz OLM]

\(3\times\left(\frac{1}{5\times8}+\frac{1}{8\times11}+....+\frac{1}{97\times100}+x\right)=\frac{319}{100}\)

\(\Rightarrow\left(\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+...+\frac{3}{97\times100}\right)+3\times x=\frac{319}{100}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{97}-\frac{1}{100}+3\times x=\frac{319}{100}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{100}+3\times x=\frac{319}{100}\)

\(\Rightarrow\frac{19}{100}+3\times x=\frac{319}{100}\)

\(\Rightarrow3\times x=\frac{319}{100}-\frac{19}{100}\)

\(\Rightarrow3\times x=3\)

\(\Rightarrow x=3:3\)

\(\Rightarrow x=1\)

Vậy x = 1