Document 436k

I create cheat sheets after giving the same lesson over and over again. This one covers the 10 series convergence tests for convergence...

Document 436k

I create cheat sheets after giving the same lesson over and over again. This one covers the 10 series convergence tests for convergence...

Document 333k

I create cheat sheets after giving the same lesson over and over again. This one covers sequences and series. Nice collection of series...

Document 21k

The file contains an explanation for finding upper limit to infinite sum $$\sum_{r=1}^{\infty}{\frac{r+2}{2^{r+1}\times r \times...

There's a famous (and probably apocryphal) story about the mathematician Carl Friedrich Gauss that goes something like this: Gauss was 9 years old, and sitting in his math class. He was a genius even at this young age, and as such was incredibly bored in his class and would always goof off and get into trouble. One day his teacher wanted to punish him for goofing off, and told him that... read more

On I.Q. tests and in other places, one is often confronted with problems of the form: “What’s the next element in the following series: 1, 4, 9, …” Technically, such questions have no right answer, because there are a multitude of ways to generate the initial elements of the series, and each way can produce a different result for how the series should continue. What is being sought is... read more

Geometric Progression A progression is another way of saying sequence thus a Geometric Progression is also known as a Geometric Sequence. A Geometric Progression is a special sequence defined by the special property that the ratio of two consecutive terms is the same for all the terms in the sequence. Whereas in Arithmetic Progression we talked of difference, here we talk of ratios... read more

Sequences and Series Sequences A sequence in mathematics is defined as an ordered list of elements (usually numbers) whose order defines some underlying property of the list. The order of the elements is very important and changing even one element would change the meaning of the entire sequence. The elements in a sequence are separated by commas and the length of a sequence is usually... read more

Arithmetic Progression A progression is another term for sequence. Therefore, Arithmetic Progressions (also known as Arithmetic Sequences) are special sequences defined by the property that the difference between any two consecutive terms of the sequence are constant. Whereas the rule for regular sequences is that the difference between consecutive terms has to have some kind of relationship,... read more

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