Why so ??

Notice this :

1×9+21\times9+2= 1111

12×9+312\times9+3= 111111

123×9+4123\times9+4= 11111111

1234×9+51234\times9+5= 1111111111

12345×9+612345\times9+6= 111111111111

123456×9+7123456\times9+7= 11111111111111

1234567×9+81234567\times9+8= 1111111111111111

12345678×9+912345678\times9+9= 111111111111111111

123456789×9+10123456789\times9+10= 11111111111111111111

Magic of mathematics

Can anyone prove the cause of the sequence

Ps: without without actual multiplication and Induction

Note by Parth Lohomi
4 years, 9 months ago

No vote yet
1 vote

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Proof: Math is awesome. And we are done.

Marc Vince Casimiro - 4 years, 9 months ago

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

Parth Lohomi - 4 years, 9 months ago

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Hint: Mathematical Induction!

Satvik Golechha - 4 years, 9 months ago

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Will you elaborate.

siddharth bhatt - 4 years, 9 months ago

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Sure. I used induction on the number of digits in the number 123.....n\overline{123.....n}, which is 11 less than the number of ones, which, in turn, is the number with which we multiply 123.....n\overline{123.....n} by, after adding 99. Firstly, I proved it true for the base case, that is, n=1n=1, then let it be true for 1,2,3,...,k1,2,3,...,k, and then consecutively proved it right for n=k+1n=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 - 4 years, 9 months ago

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

Parth Lohomi - 4 years, 9 months ago

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seems like division algorithm

Nihar Mahajan - 4 years, 9 months ago

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Isn't it awesome!!

Parth Lohomi - 4 years, 9 months ago

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

Nihar Mahajan - 4 years, 9 months ago

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