Question

Answer 1

\(\Leftrightarrow5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{x\left(x+5\right)}\right)=\dfrac{475}{96}\)

\(\Leftrightarrow1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+5}=\dfrac{475}{96}:5=\dfrac{95}{96}\)

\(\Leftrightarrow1-\dfrac{1}{x+5}=\dfrac{95}{96}\)

=>1/x+5=1/96

=>x+5=96

hay x=91

Answer 2

\(\Leftrightarrow\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{x\left(x+5\right)}=\dfrac{95}{96}\)

\(\Leftrightarrow\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{x}-\dfrac{1}{x+5}=\dfrac{95}{96}\)

\(\Leftrightarrow1-\dfrac{1}{x+5}=\dfrac{95}{96}\)

\(\Leftrightarrow\dfrac{x+4}{x+5}=\dfrac{95}{96}\)

\(\Rightarrow96\left(x+4\right)=95\left(x+5\right)\)

\(\Leftrightarrow96x+384=95x+475\)

\(\Leftrightarrow x=91\)