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?
Let’s assume we have defined the matrix rank as: “the number of linearly independent rows and columns in a matrix”. What properties of ranks follow from this definition right from the start?
First, it’s obvious that the matrix rank can be: 1, or 4, or sometimes 0. But it will definitely not be: -4, or 1/2. Okay, is that all?
“If in our research series we come across something that our mind does not want to understand well, we should stop and refrain from further unnecessary investigation of subsequent things.” DESCARTES.
What did he mean?
For the limits of many sequences with logarithms, you can confidently use the transformations and formulas for logarithms learned in high school.
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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