Let $n$ be a positive integer. Prove that for any real number $x$, $\left \lfloor nx \right \rfloor \ = \ \sum_{n-1}^{i=0}\left ( \left \lfloor x + \frac{i}{n} \right \rfloor \right )$
Charles Hermite (1822-1901): French mathematician who did brilliant work in many
branches of mathematics.
Problem of Charles Hermite
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sourav das
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You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Problem of Charles Hermite
Ha Ha, that's the Hermite's Identity.
Hint: Write $x=\lfloor x\rfloor+\{x\}$ where $\lfloor x\rfloor$ is the integer part of $x$ and $\{x\}$ is the fractional one.
If you can't do it, see this
Hint: Write $x=\lfloor x\rfloor+\{x\}$ where $\lfloor x\rfloor$ is the integer part of $x$ and $\{x\}$ is the fractional one.
If you can't do it, see this
One one thing is neutral in the universe, that is $0$.