Question

1)Cho A=\(\dfrac{2016^{2016}+2}{2016^{2016}-1}\)và B=\(\dfrac{2016^{2016}}{2016^{2016}-3}\)

So sánh A và B

2)Tính \(\dfrac{1}{2016.2015}+\dfrac{1}{2015.2014}+\dfrac{1}{2013.2014}+..+\dfrac{1}{1.2}\)

CẢM ƠN VÌ ĐÃ GIÚP MIK NHÉ

Answer 1

1. Ta có: \(\dfrac{a}{b}>1\Rightarrow\dfrac{a}{b}>\dfrac{a+m}{b+m}\left(m\in Z\right)\)

\(B=\dfrac{2016^{2016}}{2016^{2016}-3}>\dfrac{2016^{2016}+2}{2016^{2016}-3+2}=\dfrac{2016^{2016}+2}{2016^{2016}-1}=A\)

Vậy A > B

2. \(\dfrac{1}{2016.2015}+\dfrac{1}{2015.2014}+\dfrac{1}{2014.2013}+...+\dfrac{1}{1.2}\)

= \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2014.2015}+\dfrac{1}{2015.2016}\)

= \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2015}-\dfrac{1}{2016}\)

= \(1-\dfrac{1}{2016}\)

=\(\dfrac{2015}{2016}\)