Why so ??

Notice this :

$1\times9+2$ = $11$

$12\times9+3$ = $111$

$123\times9+4$ = $1111$

$1234\times9+5$ = $11111$

$12345\times9+6$ = $111111$

$123456\times9+7$ = $1111111$

$1234567\times9+8$ = $11111111$

$12345678\times9+9$ = $111111111$

$123456789\times9+10$ = $1111111111$

Magic of mathematics

Can anyone prove the cause of the sequence

Ps: without without actual multiplication and Induction

#Algebra #Equations #ProofTechniques #Awesome #Magical

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

Comments

Proof: Math is awesome. And we are done.

Marc Vince Casimiro - 6 years, 5 months ago

LOLLOlLOLOLOLOLOL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Parth Lohomi - 6 years, 5 months ago

Hint: Mathematical Induction!

Satvik Golechha - 6 years, 5 months ago

Will you elaborate.

siddharth bhatt - 6 years, 5 months ago

Sure. I used induction on the number of digits in the number $\overline{123.....n}$ , which is $1$ less than the number of ones, which, in turn, is the number with which we multiply $\overline{123.....n}$ by, after adding $9$ . Firstly, I proved it true for the base case, that is, $n=1$ , then let it be true for $1,2,3,...,k$ , and then consecutively proved it right for $n=k+1$ . I've recently learnt induction, and am new to it, so I may have made a mistake. Please correct me if I have! Cheers :)

Satvik Golechha - 6 years, 5 months ago

@Satvik Golechha – @Satvik Golechha nice!! My teacher also told me but can anyone prove it without induction??

Parth Lohomi - 6 years, 5 months ago

seems like division algorithm

Nihar Mahajan - 6 years, 5 months ago

Isn't it awesome!!

Parth Lohomi - 6 years, 5 months ago

question to which human brain can't answer #powerofmaths is 0/0 = ?

Nihar Mahajan - 6 years, 5 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}`	$\boxed{123}$