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Prove that every term in a decreasing sequence that is approaching zero is greater than or equal to 0?
In a decreasing sequence that approaches zero, each term is less than or equal to the previous term and converges to zero. Since the sequence is decreasing and approaches zero, the terms cannot dip below zero; otherwise, the sequence would not be approaching zero but would instead be diverging negatively. Therefore, every term must be greater than or equal to zero, as they cannot be less than zero while still converging to zero. Thus, all terms in the sequence are non-negative.
What else can I help you with?
Do the theorems for junior certificate maths have to be exactly right or do they just have to make sense?
There is more than one way to prove a given mathematical proposition. If the sequence of reasoning is valid, then the proof is correct. That is all that is required.
How do you prove a conjecture is false?
Prove that if it were true then there must be a contradiction.
How do you prove that 0.999999999999 is equal to one?
You cannot prove that because it's false
How do I prove Pratt's lemma?
Pratt's lemma can be proved using the concept of tree decompositions and the properties of binary trees. The lemma states that any binary tree can be represented as a unique sequence of nested parenthetical expressions. To prove this, one can construct a recursive algorithm that generates the expression for each node based on its position in the tree, ensuring that the parentheses correctly reflect the tree structure. By demonstrating that the recursive structure consistently produces valid and unique representations for the sequences, the lemma is established.
Do you need to prove he's the father?
You need to prove he's the father if you're seeking monetary compensation.
Prove that every convergent sequence is a Cauchy sequence?
The limits on an as n goes to infinity is aThen for some epsilon greater than 0, chose N such that for n>Nwe have |an-a| < epsilon.Now if m and n are > N we have |an-am|=|(am -a)-(an -a)|< or= |am -an | which is < or equal to 2 epsilor so the sequence is Cauchy.
How do you prove that the sum of a convergent sequence divided by n will converge?
You can use the comparison test. Since the convergent sequence divided by n is less that the convergent sequence, it must converge.
Why must every proposition in an argument be tested using a logical sequence?
A logical sequence in an argument is a way to prove a step has a logical consequence. Every proposition in an argument must be tested in this fashion to prove that every action has a reaction.
What is the nth term for 98 94 90 84?
To find the nth term in a sequence, we first need to identify the pattern or formula that describes the sequence. In this case, the sequence appears to be decreasing by 4, then decreasing by 6, and finally decreasing by 10. This suggests a quadratic pattern, where the nth term can be represented as a quadratic function of n. To find the specific nth term for this sequence, we would need more data points or information about the pattern.
How do you prove that if a real sequence is bounded and monotone it converges?
We prove that if an increasing sequence {an} is bounded above, then it is convergent and the limit is the sup {an }Now we use the least upper bound property of real numbers to say that sup {an } exists and we call it something, say S. We can say this because sup {an } is not empty and by our assumption is it bounded above so it has a LUB.Now for all natural numbers N we look at aN such that for all E, or epsilon greater than 0, we have aN > S-epsilon. This must be true, because if it were not the that number would be an upper bound which contradicts that S is the least upper bound.Now since {an} is increasing for all n greater than N we have |S-an|
Given an arbitrary sequence of digits how can you prove it appears somewhere in pi?
It has not yet been proven whether any arbitrary sequence of digits appears somewhere in the decimal expansion of pi.
How do you prove that the efficiency C arnot is greater than 1?
You don't. Such an efficiency can be less than 1, but it can't be greater than 1.
How do you prove that ten is a composite number?
All even numbers greater than 2 are composite.
Are -14 and -23 negative integers prove your answer?
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How can you determine when a function is increasing or decreasing?
Assuming the function is linear, the direction of the function can be determined by the coefficient's sign:[y = mx + b]Where m is the coefficient of x, if m is negative, then the function is increasing. If m is positive, the function is decreasing (this relationship is rather complicated and requires advanced calculus to prove).
How can you prove that the is the sum of the lengths of any two sides of a triangle always greater than the length of the third one?
Simply measure them.
What statement do you need to prove is a rectangle?
The length of a rectangle is greater than its width and it has 2 pairs of parallel sides with 4 interior right angles.
