\(=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{n.\left(n+1\right)}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{n.\left(n+1\right)}\)
mình giải nhé:
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{n\left(n+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{n\left(n+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{n\left(n+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{n\left(n+1\right)}\right)=\frac{2015}{2016}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{n}-\frac{1}{n+1}\right)=\frac{2015}{2016}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{n+1}\right)=\frac{2015}{2016}\)
\(\Leftrightarrow1-\frac{2}{n+1}=\frac{2015}{2016}\Leftrightarrow\frac{2}{n+1}=\frac{1}{2016}\)
\(\Leftrightarrow n+1=4032\Leftrightarrow n=4031\)
Xong rồi nhé ^ ^ chúc bạn học tốt!
chậc gõ lâu quá. bạn kia nhanh hơn mình rồi
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