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

clarko

New member
Joined
Mar 9, 2023
Messages
4
Hi,
How I can find the exact value of this sum using binomial coefficient ?
k0xk/5\sum_{k \geq 0} x^{\lceil \sqrt{k/5} \rceil}
 
Hello. Please show what you've started or explain why you're stuck. Thank you!

PS: We've repaired your LaTeX tags. Please see the LaTeX thread on the News board, for information on how to invoke LaTeX at this forum.

  \;
 
Hi,
How I can find the exact value of this sum using binomial coefficient ?
k0xk/5\sum_{k \geq 0} x^{\lceil \sqrt{k/5} \rceil}
Consider the ceiling function k5\left\lceil {\dfrac{k}{5}} \right\rceil for k=1 to 25 is 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5k=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}
So we need an upper bound for the index kk in the summation. SEE THIS
 
Top