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# 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
2 years, 3 months ago

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Proof: Math is awesome. And we are done. · 2 years, 3 months ago

LOLLOlLOLOLOLOLOL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! · 2 years, 3 months ago

Hint: Mathematical Induction! · 2 years, 3 months ago

Will you elaborate. · 2 years, 2 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 :) · 2 years, 2 months ago

@Satvik Golechha nice!! My teacher also told me but can anyone prove it without induction?? · 2 years, 2 months ago

seems like division algorithm · 2 years, 3 months ago

Isn't it awesome!! · 2 years, 3 months ago

question to which human brain can't answer #powerofmaths is 0/0 = ? · 2 years, 3 months ago

Comment deleted Apr 12, 2015

well! then all questions in this world can be answered in this format .. :P · 2 years, 3 months ago

Lololololol!! · 2 years, 3 months ago