Question

TÍNH 

A = \(\frac{4}{1.2}\)+ \(\frac{4}{2.3}\)+ \(\frac{4}{3.4}\)+  ...........+  \(\frac{4}{2014.2015}\)

Answer 1

Ta có: \(A=\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+...+\frac{4}{2014.2015}\)

\(=1\left(\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{2014.2015}\right)\)

\(=1\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2015}\right)\)

\(=1\left(1-\frac{1}{2015}\right)\)

\(=1\left(\frac{2015}{2015}-\frac{1}{2015}\right)-1\left(\frac{2014}{2015}\right)=\frac{2014}{2015}\)

Vậy.....

Answer 2

\(A=\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+....+\frac{4}{2014.2015}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2014}-\frac{1}{2015}\)

\(A=\frac{1}{1}-\frac{1}{2015}=\frac{2015}{2015}-\frac{1}{2015}=\frac{2014}{2015}\)

Answer 3

Ta có: 

A = \(\frac{4}{1.2}+\frac{4}{2.3}+...+\frac{4}{2014.2015}\)

=\(4.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2014.2015}\right)\)

=\(4.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2014}-\frac{1}{2015}\right)\)

=\(4.\left(\frac{1}{1}-\frac{1}{2015}\right)\)

=\(4.\frac{2014}{2015}\)

=\(\frac{8056}{2015}\)

Answer 4

BẠN CỘNG TÁC VIÊN TTH LÀM SAI RỒI NHÉ

\(\frac{4}{1.2}+\frac{4}{2.3}+...+\frac{4}{2015.2015}\)

\(=4\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2014.2015}\right)\)

\(=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{2014}+\frac{1}{2014}-\frac{1}{2015}\right)\)

\(=4\left(1-\frac{1}{2015}\right)=\frac{4.2014}{2015}=\frac{8056}{2015}\)