Question

[Nguyễn Mai Hương]

Cho đẳng thức:x.(x+1).(x+2).(x+3).....(x+2016)=2016    (với x>0)

Chứng tỏ rằng:x<\(\frac{1}{2015}\)

Answer 1

[le bao truc]

\(A=\left(x+1\right).\left(x+2\right).\left(x+3\right)...\left(x+2016\right)=2016\)
\(A=x\left(1+2+3+...+2016\right)=2016\)
\(A=x\cdot\frac{\left(2016+1\right).2016}{2}=x\cdot2033136=2016\)
\(\Rightarrow x=2016:2033136=\frac{2}{2017}\)
\(\Rightarrow\frac{2}{2017}< \frac{1}{2015}\)
\(\Rightarrow x< \frac{1}{2015}\)

Answer 2

[le bao truc]

mik nhầm rồi! Xin lỗi nha