Question

Tính nhanh:

5/1×4+5/4×7+.....+5/2014×2017

Giúp mình với

Answer 1

\(\frac{5}{1\cdot4}+\frac{5}{4\cdot7}+...+\frac{5}{2014\cdot2017}\)

\(=\frac{5}{3}\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+...+\frac{3}{2014\cdot2017}\right)\)

\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)

\(=\frac{5}{3}\left(1-\frac{1}{2017}\right)\)

\(=\frac{5}{3}\cdot\frac{2016}{2017}=\frac{10080}{6051}=1\frac{4029}{6051}\)

Answer 2

\(S=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{2014.2017}\)
\(S=5\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(S=5.3\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(S=15.\left(\frac{1}{1}-\frac{1}{2017}\right)=15\cdot\frac{2016}{2017}=\frac{30240}{2017}\)