Question

S=1/2011+1/2012+1/2013+...+1/2021+1/2022+1/2023
P=1/2022+2/2021+3/2020+...+12/2011+13/1
hãy tính giá trị P/S

Answer 1

\(P=\dfrac{1}{2022}+\dfrac{2}{2021}+\dfrac{3}{2020}+...+\dfrac{12}{2011}+\dfrac{13}{1}\\ P=\left(\dfrac{1}{2022}+1\right)+\left(\dfrac{2}{2021}+1\right)+.....+\left(\dfrac{12}{2011}+1\right)+1\\ P=\dfrac{2023}{2022}+\dfrac{2023}{2021}+...+\dfrac{2023}{2011}+\dfrac{2023}{2023}\\ P=2023\cdot\left(\dfrac{1}{2022}+\dfrac{1}{2021}+...+\dfrac{1}{2022}+\dfrac{1}{2023}\right)\)

\(\dfrac{P}{S}=\dfrac{2023\cdot\left(\dfrac{1}{2023}+\dfrac{1}{2022}+\dfrac{1}{2021}+...+\dfrac{1}{2011}\right)}{\dfrac{1}{2011}+\dfrac{1}{2012}+...+\dfrac{1}{2023}}\\ =2023\)

Answer 2

S=1/2011+1/2012+1/2013+...+1/2021+1/2022
hãy tính giá trị biểu thức của S