# Dangerous sigma

For any positive integer $n$, let $n'$ denote the closest integer to $\sqrt n$, then $\displaystyle \sum_{n=1}^\infty \frac{2^{n'} + \left(\frac12 \right)^{n'}}{2^n} = \ ?$

I don't seem to understand how to even approach this question, any help would be appreciated.

Edit: The question has been turned into a problem by @Chew-Seong Cheong sir. It can be accessed here.

8 months, 3 weeks ago

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Using Wolfram Alpha the answer is 3. See here.

- 8 months, 2 weeks ago

- 8 months, 2 weeks ago

I would not want to try. No algebraic method to handle nearest integers $\lfloor x + \frac 12 \rfloor$.

- 8 months, 2 weeks ago

OK. I will try if I got I will set it as a question. I have some idea now.

- 8 months, 2 weeks ago

Check out the solution here.

- 8 months, 2 weeks ago

Thank you sir! Very grateful.

- 8 months, 2 weeks ago

Did you delete the solution to my recent problem? @Chew-Seong Cheong

- 6 months ago

Yes, I don't think my solution was correct.

- 6 months ago