\(\left(x+\frac{1}{2\cdot3}\right)+\left(x+\frac{1}{3\cdot4}\right)+....+\left(x+\frac{1}{15\cdot16}\right)=\frac{39}{16}\)
\(\Leftrightarrow\left(x+x+x+....+x\right)+\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{15\cdot16}\right)=\frac{39}{16}\)
\(\Leftrightarrow14x+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{15}-\frac{1}{16}\right)=\frac{39}{16}\)
\(\Leftrightarrow14x+\left(\frac{1}{2}-\frac{1}{16}\right)=\frac{39}{16}\)
\(\Leftrightarrow14x+\frac{7}{16}=\frac{39}{16}\)
\(\Leftrightarrow14x=2\)
\(\Leftrightarrow x=\frac{1}{7}\)
[X+1/2x3] + [X+1/3x4] + ...+[X+ 1/15x16]=39/16
tìm X