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Here are a few challenging proofs to be done using Principles Of Mathematical Induction. I will be editing this note hereafter, by keeping new Induction Challenges, most probably one new challenge per week. Check these out and post your solutions in the comments below 📝 📬 📮 !

Challenge 1 -> Prove that the $n^{th}$ term in the Fibonacci series is :-

$u_{n} = \dfrac {1}{\sqrt {5}}\left[ \left (\dfrac {1+\sqrt {5}}{2}\right) ^{n}-\left( \dfrac {1-\sqrt {5}}{2}\right) ^{n}\right]$

Challenge 2 -> Prove the rule of transitivity in inequalities using only the definitions and induction principles.

#MathematicalInduction #Proofs #Challenge #CoolMath

Easy Math Editor

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`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`	$\sum_{i=1}^3$
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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}`	$\boxed{123}$

My 50 50 50 followers note !

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My $50$ followers note !