dear all, lets consider a length L and divide it into N number of small segments uniformly. Then the length of every segment should be L/N.
then we add these segments up, which is
L=[itex]\sum[/itex][itex]\frac{L}{N}[/itex]
then we take the limit N→[itex]\infty[/itex] at both sides, this means
[itex]lim_{N\rightarrow\infty}[/itex]L=[itex]lim_{N\rightarrow\infty}[/itex][itex]\sum[/itex][itex]\frac{L}{N}[/itex]
the left hand is still L, and right hand will become, at the limit, [itex]\underbrace{0+0+0+...}_{infinite}[/itex]
therefore, the sum of infinite number of zeros will lead to a finite number ? This is my question. I hope someone could give some idea. Thank you !
then we add these segments up, which is
L=[itex]\sum[/itex][itex]\frac{L}{N}[/itex]
then we take the limit N→[itex]\infty[/itex] at both sides, this means
[itex]lim_{N\rightarrow\infty}[/itex]L=[itex]lim_{N\rightarrow\infty}[/itex][itex]\sum[/itex][itex]\frac{L}{N}[/itex]
the left hand is still L, and right hand will become, at the limit, [itex]\underbrace{0+0+0+...}_{infinite}[/itex]
therefore, the sum of infinite number of zeros will lead to a finite number ? This is my question. I hope someone could give some idea. Thank you !
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