math problem

I want to ask what is mathematical induction and how it works.Why we use k and (k+1)?

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Have you read the summary pages on the technique of Mathematical Induction?

Calvin Lin Staff - 7 years, 7 months ago

The dominoes effect: if one dominoe falls, the other dominoes fall.

Bruce Wayne - 7 years, 7 months ago

It is quite simple, Suppose u discovered a new formula in Math. And u wanna test whether the formula holds for every n or not. So, u can test it by ind princip. First verify. Is it true for n=1, p(n) means formula holds for n, then assume p(k) is true and show that it.follows p(k+1).
You have already proved p(1) is true, and p(k)=> p(k+1), it means formula is true for 2, and hence for 3, and the chain continues... This is mth indctn and by this the formula is true for every n

Surendra Ratha - 7 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$