Question

cho a=1.2+2.3+3.4+...+2017.2018 và b=2018^3/3

so sanhs a va b

Answer 1

\(A=1.2+2.3+3.4+...+2017.2018\)

\(3A=1.2.3+2.3.3+3.4.3+...+2017.2018.3\)

\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+2017.2018.\left(2019-2016\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2017.2018.2019-2016.2017.2018\)

\(\Rightarrow3A=2017.2018.2019\)

\(\Rightarrow A=\dfrac{2017.2018.2019}{3}\)

\(A=\dfrac{2017.2018.2019}{3};B=\dfrac{2018^3}{3}=\dfrac{2018.2018.2018}{3}\)

\(A=2739315938;B=2739316611\)

\(\Rightarrow A< B\)