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Limit of a sequence

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Troubles with Indeterminate Symbols (VIDEO)

24 July 2024 / Krystian Karczyński

This post is a kind of response to the question: "I don't understand something and I need an explanation, why do you simplify 'n'? I mean that n/n is an indeterminate symbol (infinity over infinity) help because I'm already lost with this." Understanding what indeterminate symbols REALLY are can be quite tricky. It also raises many questions about what you "can" and "can't" do with them.

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The Symbol 0 in the Limits of Functions and Sequences

27 June 2024 / Krystian Karczyński

When working with limits of functions and sequences, we frequently come across various mathematical oddities, such as: 0/0 or 1/0. The question is - what do they mean? I often come across completely incorrect opinions like: "at higher levels in mathematics, you can divide by 0".

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The Limit of a Sequence with Two Mixed Sums of Arithmetic Sequences

26 June 2024 / Krystian Karczyński

Sequence limits sometimes use formulas for the sum of arithmetic or geometric sequences. It's worse if these sequences are given in a "mixed" way in one line, like here.

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Limit of a Sequence with an Infinite Sum

21 June 2024 / Krystian Karczyński

Let's take the following sequence limit approaching infinity: (1/{12}+1/{23}+1/{3*4}+...+1/{(n-1)*n}). In the problem, we kind of feel that we need to use sequence sum formulas (arithmetic or geometric), but unfortunately, this sequence is neither arithmetic nor geometric... So what to do?

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Limits of Sequences with Logarithms

18 June 2024 / Krystian Karczyński

For the limits of many sequences with logarithms, you can confidently use the transformations and formulas for logarithms learned in high school.

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An Unconventional Sequence Limit with a Formula for the Number e as a Result

18 June 2024 / Krystian Karczyński

Learn step by step how to solve unconventional sequence limits using the formula for the number e. Examples, explanations, and methods for solving equations that help understand how to apply the formula for the number e in various situations. Ideal article for students and math enthusiasts.

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The Limit of a Sequence Posing as a Limit Involving the Number e

29 April 2024 / Krystian Karczyński

Learn how to solve problems with sequence limits correctly when the number e is involved. The article discusses problems and differences arising from polynomials raised to powers, and when and how to use appropriate formulas for limits with the number e. You'll also understand how routines in limit calculations can lead to mistakes and how to avoid them.

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