Question

tính nhanh   \(B=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{2014.2017}\)

Nhanh lên nha mai mk thi rồi

Answer 1

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

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

\(B=\frac{5}{3}.\frac{2016}{2017}=\frac{10080}{6051}\)

Answer 2

\(B=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{2014.2017}\)

\(3M=5\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{2014.2017}\right)\)

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

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

\(3M=5.\frac{2016}{2017}\)

\(3M=\frac{10080}{2017}\)

\(\Rightarrow M=\frac{3360}{2017}\)

Answer 3

Ta có: 

\(B=\frac{5}{1.4}+\frac{5}{4.7}+.....+\frac{5}{2014.2017}\)

\(\Rightarrow B.\frac{3}{5}=\frac{3}{1.4}+\frac{3}{4.7}+.....+\frac{3}{2014.2017}\)

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

\(=1-\frac{1}{2017}\)

\(=\frac{2016}{2017}\)

\(\Rightarrow B=\frac{2016}{2017}:\frac{3}{5}\)

\(=\frac{3360}{2017}\)

Vậy B \(=\frac{3360}{2017}\)~~~~~

Answer 4

\(B=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{2014.2017}\)

\(\Rightarrow B=5\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{2014.2017}\right)\)

\(\Rightarrow3B=5\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{2014.2017}\right)\)

\(\Rightarrow3B=5\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)

\(\Rightarrow3B=5\left(1-\frac{1}{2017}\right)\)

\(\Rightarrow3B=5.\frac{2016}{2017}\)

\(\Rightarrow B=\frac{5.2016\div3}{2017}\)

\(\Rightarrow B=\frac{3360}{2017}\)