Main post link -> https://brilliant.org/assessment/techniques-trainer/mathematical-induction/

Learn about mathematical induction, a method of proof typically used to establish that a given statement is true for all natural numbers.

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`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestThe good part is "We now sit back and drink a cup of coffee" that really nice sir :)

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At the end of the first worked example:

{We now sit back and drink a cup of coffee.]

You're mixing up your brackets. :)

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Sir, can you tell me, that how many types of induction are there?

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The works 'type' could either refer to various types of applications (first paragraph), or various mathematical topics where induction can be applied (second paragraph).

I have broadly identified 5-6 different applications that are based off the underlying idea of Induction, and will plan to explore them in the upcoming weeks. For example, students generally have heard of the Non-standard Induction, where you use several base cases instead of just 1, or the Strong Induction, where you use every preceding statement, instead of just \(P_k\).

Almost every mathematical topic has a problem which yields to an inductive approach. In the post, I've presented a question on summation of series, and another on divisibility. Other areas include recurrence relations, inequalities, functional equations, integration/differentiation, games, etc.

Edit: Here are various 'types' of induction. This might not be a complete list.

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there are three types of induction, first principle induction second principle induction third principle induction. if u want to know about them, just reply here.

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The first principle is simple induction, and the second principle is the Strong Induction that Calvin alludes to in his comment.

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