Trả lời :
\(E=-\left(\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+...+\frac{4}{n\left(n+4\right)}\right)\)
\(\Rightarrow E=-\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{n}-\frac{1}{n+4}\right)\)
\(\Rightarrow E=-\left(1-\frac{1}{n+4}\right)\)
\(\Rightarrow E=1+\frac{1}{n+4}\)
P/s : Sai thì thông cảm nha chị. Dạng này lâu chưa làm nên không nhớ rõ.
\(E=-\frac{4}{1.5}-\frac{4}{5.9}-\frac{4}{9.11}-...-\frac{4}{\left(n-4\right)n}\)
\(\Rightarrow E=-\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.11}+...+\frac{4}{\left(n-4\right)n}\right)\)
\(\Rightarrow E=-\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{n-4}-\frac{1}{n}\right)\)
\(\Rightarrow E=-\left(1-\frac{1}{n}\right)\)
\(\Rightarrow E=-1+\frac{1}{n}\)
cảm ơn các bạn rất nhìu