Just for fun

Posted on Tue 03 April 2018 in Fun

Random thoughts

Its nice to see the following:

$$9.1\times{9.1} + 9.1 = 91.91$$

I pondered a bit more and it turns out be of the following pattern

$$99.1\times{99.1} + 99.1 = 9919.91$$

$$999.1\times{999.1} + 999.1 = 999199.91$$

$$9999.1\times{9999.1} + 9999.1 = 99991999.91$$

The pattern in result (RHS) emerges out to be you repeat the number in LHS (9.1) twice without decimals and put the decimal 2^nd from the right.

Still trying to find a mathematical proof that explains why the whole process only has only two digits (9 and 1)

Explanation:

$$9.1\times{9.1} + 9.1 = 9.1\times{(9.1 + 1)} = 9.1\times{10.1} = 9.1\times{(10 + 0.1)}$$

$$ = 91 + 0.91 = 91.91$$

True for others also: the reason behind no having any other digit is because only 10 and 0.1 are being used in multiplication.

Could you guess the next number:

$$1, 2, 720, ?$$

Credits: Joe Blitzstein (Harvard Stats 110), will post the youtube link once I find it