Câu trả lời:
Xét mẫu:
\(1+\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+...+2012}\)
= \(1+\frac{1}{3}+\frac{1}{6}+....+\frac{1}{2025078}\)
= \(1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2012.2013}\right)\)
= \(1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2012}-\frac{1}{2013}\right)\)
= \(1+2.\left(\frac{1}{2013}\right)\)
= \(\frac{4024}{2013}\)
=> E = \(\frac{2.2012}{\frac{4024}{2013}}\)
=> E = \(4024.\frac{2013}{4024}\)
=> E = 2013