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The value of the expression

\[\displaystyle{\lim _{ n\rightarrow \infty }{ \frac { 1 }{ n+1 } } +\frac { 1 }{ n+2 } +.....+\frac { 1 }{ n+5n } }\]

can be written as ...

Is there any periodic function with fundamental period less than 100 that satisfies the equation

\[f(x+1)+f(x-1)=2(\cos{\frac{\pi}{2018}}) f(x)?\]

Inspiration.

Given a real-valued function \(f(x)\) that is defined over all real values \(x\) and satisfies ...

Is there a nowhere continuous function satisfying the following functional equation? \[f(x-1)+f(x+1)=\sqrt{3}f(x)\] Justify your answer.

Note: A real-valued function defined on the ...

If \(f(x)\) is a function such that \(f(x-1) + f(x+1) = \sqrt{3} f(x)\) and \(f(5)= 10\), then what is the sum of digits of ...

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