2
$\begingroup$

Let $[x]$ be the nearest integer to $x$. (for $x=n+\frac{1}{2}, n \in N$, let $[x]=n$).

Find the value of $$\displaystyle\sum_{m=1}^{\infty} [\sqrt m]^{-3}$$

$\endgroup$
  • $\begingroup$ Do you have any ideas about what numbers are $[\sqrt m] ^2$? $\endgroup$ – Karolis Juodelė Jun 28 '14 at 13:40
2
$\begingroup$

Hint: note that $[m]=1$ twice, it equals $2$ four times (from $3$ through $6$). How many times does it equal $k$?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.