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Easy Math Editor

`*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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TopNewestYou are referring to the First Principle of Finite Induction, which can be proved by contradiction.

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why in induction problems we assume that f(n) is true and then proceed.....this is only the thing to prove

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I would like to explain the whole principle: First we check for \(f(1)\), if it is true we proceed.Then we assume that it is true for a natural number k.Then we check whether it is true for k+1.If it is also true then our given expression is true for all natural numbers.We assumed that it is true for k then we proceed, but previously we checked that it is true for 1.So in this case k=1.Now we prove that it is true for k+1,so it is true for k=2.So now we proved that it is true for 2.Now ,let k=2 as k=2 satisfies the condition,so we again prove that it is true for k+1 i.e 3.Again we let k=3 and prove for k=4.The cycle goes on and on which shows that expression is true for all natural numbers.Let me know where I am wrong.Yes I accept my weak english.Sorry for it.

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thnks kevin ,and about your english ,its absolutely flawless

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