Something I can't seem to prove

  • Thread starter Skynt
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In summary, there are several factors that can make something difficult to prove, including lack of evidence, complexity, and limitations in understanding or technology. However, in the field of science, something can be considered proven beyond a reasonable doubt if it has been extensively tested and supported by multiple studies with consistent results. Scientists use the scientific method to determine the truth or validity of a claim, and if something cannot be proven, it does not necessarily mean it is false. Some phenomena may not be able to be proven using the scientific method, and other methods of investigation may be used in these cases.
  • #1
Skynt
39
1
It should be really simple, but I think the algebra is bogging me down:

[tex]\frac{n!}{(n-i)! i!} + \frac{n!}{[n-(i+1)]! (i+1)!} = \frac{(n+1)!}{(n-i)! (i+1)!}[/tex]

Can anyone show me the process of proving this? I don't see how the two expressions are equal...

essentially I can't get rid of the [n - (i + 1)]! term when I try to combine the two fractions and expand things.
 
Last edited:
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  • #2
Notice that [n - i] * [n - (i + 1)]! = [n - i]!.
 
  • #3
obviously *bangs head* thanks!
 
  • #4
That is, by the way, the formula used for producing Pascal's triangle.
 

1. What makes something difficult to prove?

There are several factors that can make something difficult to prove, such as lack of evidence, complexity of the subject, or the inability to replicate results. It could also be due to limitations in our current understanding or technology.

2. Can something be proven beyond a reasonable doubt?

Yes, in the field of science, something can be considered proven beyond a reasonable doubt if it has been extensively tested and supported by multiple studies with consistent results. However, there is always room for new evidence and further research to potentially change our understanding.

3. How do scientists determine if something is true or not?

Scientists use the scientific method to determine the truth or validity of a claim. This involves making observations, forming a hypothesis, conducting experiments, analyzing data, and drawing conclusions. The results are then peer-reviewed and replicated by other scientists to ensure accuracy.

4. What happens if something cannot be proven?

If something cannot be proven, it does not necessarily mean it is false. It may just mean that there is not enough evidence to support it at the current time. Scientists may continue to research and gather evidence to try to prove or disprove the claim.

5. Can something be proven in all fields of science?

No, not all things can be proven in all fields of science. Some phenomena, such as historical events or human behavior, may not be able to be tested and proven using the scientific method. In these cases, other methods of investigation and analysis may be used to understand and explain the subject.

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