# 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

Note by Parth Lohomi
5 years, 10 months ago

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Hint: Mathematical Induction!

- 5 years, 10 months ago

Will you elaborate.

- 5 years, 10 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 :)

- 5 years, 10 months ago

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

- 5 years, 10 months ago

Proof: Math is awesome. And we are done.

- 5 years, 10 months ago

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

- 5 years, 10 months ago

seems like division algorithm

- 5 years, 10 months ago

Isn't it awesome!!

- 5 years, 10 months ago

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

- 5 years, 10 months ago