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.

No vote yet

14 votes

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

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

Log in to reply

At the end of the first worked example:

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

You're mixing up your brackets. :)

Log in to reply

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

Log in to reply

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.

Log in to reply

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.

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply