Question

tính giá trị của các biểu thức sau(casio)

a/\(B=\dfrac{1}{\sqrt{x}+\sqrt{x+1}}+\dfrac{1}{\sqrt{x+1}+\sqrt{x+2}}+\dfrac{1}{\sqrt{x+2}+\sqrt{x+3}}+....+\dfrac{1}{\sqrt{x+2015}+\sqrt{x+2016}}v\text{ới}x=2017\)

Answer 1

\(B=B_1+B_2+...+B_{2016}\)

\(B_1=\dfrac{\sqrt{x+1}-\sqrt{x}}{\left(\sqrt{x}+\sqrt{x+1}\right)\left(\sqrt{x+1}-\sqrt{x}\right)}=\dfrac{\sqrt{x+1}-\sqrt{x}}{x+1-x}\)

\(B_1=\sqrt{x+1}-\sqrt{x}\)

\(B_2=\sqrt{x+2}-\sqrt{x+1}\)

\(B_3=\sqrt{x+3}-\sqrt{x+2}\)

...

\(B_{2015}=\sqrt{x+2015}-\sqrt{x+2014}\)

\(B_{2016}=\sqrt{x+2016}-\sqrt{x+2015}\)

\(B=\sqrt{x+2016}-\sqrt{x}\)

\(B\left(2017\right)=\sqrt{2017+2016}-\sqrt{2017}\)