If $x=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{1000000}}$, what is the value of $\lfloor{x}\rfloor$?

47 Views Asked by At

If $x=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{1000000}}$, what is the value of $\lfloor{x}\rfloor$?

I'm sure I'm supposed to use telescoping series to solve this problem, but I don't know how to start. Can someone give me a hint?