Question

Tìm x: 1/(x-1).(x+3)+1/(x+3).(x+7)+...+1/(x+76).(x+80)=-81/320

Answer 1

\(\frac{1}{\left(x-1\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+7\right)}+....+\frac{1}{\left(x+76\right).\left(x+80\right)}=-\frac{81}{320}\)

\(\Rightarrow\frac{4}{\left(x-1\right)\left(x+3\right)}+\frac{4}{\left(x+3\right)\left(x+7\right)}+...+\frac{4}{\left(x+76\right)\left(x+80\right)}=\frac{-81}{80}\)

\(\Rightarrow\frac{1}{x-1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+7}+...+\frac{1}{x+76}-\frac{1}{x+80}=\frac{-81}{80}\)

\(\Rightarrow\frac{1}{x-1}-\frac{1}{x+90}=\frac{-81}{80}\)

Vì \(\frac{-81}{80}< 0\Rightarrow\frac{1}{x-1}< \frac{1}{x+90}\)

\(\Leftrightarrow x-1>x+90\)( luôn sai \(\forall x\in R\))

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