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Does the series sigma evaluated from n equals 1 to infinity of 1 over n times the quantity the natural log of n squared converge or diverge?
Wiki User
∙ 7y ago
Diverge!
Wiki User
∙ 7y ago
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What is infinity to the infinity?
Presuming you are using limits, the exponentiation of two limits which diverge to infinity, also diverge to infinity. Or, using shorthand notation: ∞∞= ∞
What is infinity times infinity minus infinity?
Firstly, infinity is not a number (at least in lower level mathematics). You must instead use the language of limits to describe infinity. Using limits, a function which diverges to infinity multiplied by a function which diverges to infinity has a product which also diverges to infinity. However, taking this product, and subtracting away a function which diverges to infinity is "of indeterminate form". It might converge to zero, it might be diverge to positive infinity, it might diverge to negative infinity, or it might converge to a constant. In order to figure out which one of these possibilities applies, you must get the indeterminate form into the form infinity divided by infinity or 0/0 and then apply L'Hospital's rule. Edit: Just a pet peeve of mine. It's L'Hôpital, not L'Hospital. Even textbooks don't spell it right.
What s the noun from diverge?
The noun forms for the verb to diverge are divergence and the gerund, diverging.
What is a synonym for diverge?
Diverge means move away from each other and go in different directions. Synonyms of the word diverge are split, separate, branch off, and bifurcate.
When does the methods fail to find the solutions?
Methods for finding solutions may fail for a variety of reasons:there may not be a solution;there may not be a solution in the relevant domain - for example 2x = 3 has no solution if x must be an integer, but it does have a colution if x is allowed to be a fraction.the method may diverge away from the solution rather than converge towards it.
What is opposite of converge?
diverge
What are some antonyms for diverge?
Join, converge and coalesce are antonyms of diverge
What is infinity to the infinity?
Presuming you are using limits, the exponentiation of two limits which diverge to infinity, also diverge to infinity. Or, using shorthand notation: ∞∞= ∞
Is infinity divided by infinity equal to infinity?
First off, infinity is not a number in conventional mathematics. In Calculus, you can work with infinity through the language of limits. It is important to note that when we use the shorthand: ∞/∞ What we are REALLY saying is "the limit of a function which diverges to infinity divided by the limit of a function which diverges to infinity". We are not actually saying "infinity divided by infinity". Now that THAT is out of the way, we can get to the answer. ∞/∞ is of indeterminate form, meaning that the division could converge to 0, it could converge to 1, it could converge to an arbitrary constant, or it could diverge to infinity. In order to figure out which of these cases is true, you need to apply L'Hospital's rule, by taking the derivative of the numerator and the denominator (separately).
What is infinity times infinity minus infinity?
Firstly, infinity is not a number (at least in lower level mathematics). You must instead use the language of limits to describe infinity. Using limits, a function which diverges to infinity multiplied by a function which diverges to infinity has a product which also diverges to infinity. However, taking this product, and subtracting away a function which diverges to infinity is "of indeterminate form". It might converge to zero, it might be diverge to positive infinity, it might diverge to negative infinity, or it might converge to a constant. In order to figure out which one of these possibilities applies, you must get the indeterminate form into the form infinity divided by infinity or 0/0 and then apply L'Hospital's rule. Edit: Just a pet peeve of mine. It's L'Hôpital, not L'Hospital. Even textbooks don't spell it right.
What is meant by converge and diverge?
Converge means coming together or meeting at a common point, while diverge means branching off or moving apart in different directions. In mathematical terms, if a sequence or series of values approaches a specific number as they progress, they are said to converge. On the other hand, if the values in a sequence or series move further apart or do not approach a specific number, they are said to diverge.
Define power of the lens?
It is the ability of a lens to converge or diverge a ray of light.
Do Light Rays converge or diverge?
Light rays can converge or diverge based on the type of lens or mirror they pass through. Converging lenses and concave mirrors cause light rays to converge, focusing them at a single point known as the focal point. Diverging lenses and convex mirrors cause light rays to diverge, spreading them out.
Why are lenses and mirrors used in optical tools?
Because they converge, diverge and reflect light.
What are some words that end with the suffix verge?
Converge, Diverge, Submerge, Emerge.
True or false rays reflected from a convex mirror always converge?
False. Rays reflected from a convex mirror do not always converge. In the case of a convex mirror, the reflection causes the rays to diverge away from each other.
Do negative lenses diverge?
Actually the negative lens just sits there. It causes a parallel beam of light to diverge. It causes a convergent beam to converge less. It causes a divergent beam to diverge more.
