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 2nd 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.

Orders: not so obvious

Could you guess the next number:

$$1, 2, 720, ?$$

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