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topengonzo
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summation from k to n of 1/((k-1)!(k+1)) < 1/k! using induction
How can i write it to look math
How can i write it to look math
mathman said:You have 2 integer variables, k and n. What is the induction variable?
This is how I would interpret what you wrote:topengonzo said:summation from k to n of 1/((k-1)!(k+1)) < 1/k! using induction
How can i write it to look math
This is how I would interpret what you wrote:
∑r=kn1(k−1)!(k+1)<1k!
This is "the sum from k to n of 1/((k-1)!(k+1))" -- and it is false.This is what I think you meant:
∑r=kn1(r−1)!(r+1)<1k!
This is true for all finite integers k>0, n≥k. You don't need recursion to prove this.
This is the homework section of PhysicsForums. You need to show some work.topengonzo said:Yes the second one you wrote is what i exactly mean. How do I prove it? Also I think if i set n -> infinity (find lim at infinity), I would get = instead of < . Am I correct?
D H said:This is the homework section of PhysicsForums. You need to show some work.
I will give a hint: Induction is not the way to go here. Simply find the value of the series.
Yes!topengonzo said:[tex]\sum_{r=k+1}^{n+1} \frac {r-1} {(r)!} < \frac 1 {k!}[/tex]
Is this correct?
No![tex]\sum_{r=0}^{inf} \frac {r-1} {(r)!}[/tex] = e-e=0
And then I take out term from 0 to k?
Prove every positive rational number x can be expressed in ONE way in the form
x= a1 + a2/2! + a3/3! + ... + ak/k!
where a1,a2,...,ak are integers and 0<=a1,0<=a2<2,...,0<=ak<k
Yes, the scientific method is a systematic approach to conducting experiments and gathering evidence to support or refute a hypothesis.
Reliable evidence can be tested and replicated, and the results should be consistent. It should also come from unbiased and well-controlled experiments.
This is a common occurrence in science and can lead to new discoveries. It is important to analyze and interpret the results objectively and consider alternative explanations.
No, science relies on evidence and the best available explanations, but there is always room for new evidence or theories to change our understanding of a topic.
Scientific communication can take many forms, such as publishing in scientific journals, presenting at conferences, or using media platforms. It is important to present the evidence and conclusions accurately and clearly.