How I can find the exact value of this sum using binomial coefficient

[clarko]

Hi,
How I can find the exact value of this sum using binomial coefficient ?
[math]\sum_{k \geq 0} x^{\lceil \sqrt{k/5} \rceil}[/math]

 

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[Steven G]

Can you please define k?

 

[pka]

Hi,
How I can find the exact value of this sum using binomial coefficient ?
[math]\sum_{k \geq 0} x^{\lceil \sqrt{k/5} \rceil}[/math]

Consider the ceiling function [imath]\left\lceil {\dfrac{k}{5}} \right\rceil[/imath] for [imath]k=1\text{ to }25\text{ is } {1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5}[/imath]
So we need an upper bound for the index [imath]k[/imath] in the summation. SEE THIS