Question

Cho : A= 3/1.2.3+3/2.3.4+3/3.4.5+.....+3/2015.2016.2017    so sánh A với1

 Giúp mk với nhé!

Answer 1

\(A=\frac{3}{1.2.3}+\frac{3}{2.3.4}+\frac{3}{3.4.5}+...+\frac{3}{2015.2016.2017}\)

\(A=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{3}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+\frac{3}{2}.\left(\frac{1}{3.4}-\frac{1}{4.5}\right)+...+\frac{3}{2}.\left(\frac{1}{2015.2016}-\frac{1}{2016.2017}\right)\)

\(A=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2015.2016}-\frac{1}{2016.2017}\right)\)

\(A=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2016.2017}\right)\)

\(A=\frac{3}{4}-\frac{3}{2.2016.2017}< 1\)