5 cool math tricks ft. Technicality

I knew that 11 trick....


I also found this:
If you see the first row of the pascal's triangle as row 0, and after that is row 1 and so on, you can follow the term 11^n for the row n that you want to calculate...

although it only DIRECTLY works for the rows in the single digits...

BUT IT WORKS!

n=0: 1
n=1: 11
n=2: 121
n=3: 1331
n=4: 14641
n=5: 15101051 ... but 11^5 turns out to be 161051... since the 10s merged with the other numbers..

BUT: If you got a lot of spare time and are good at remembering things... you can use 

e^.1 ≈ 1.10517 ≈ 1.105 ≈ 1.1

1.1 is just 11 / 10... so you can use the pascal's triangle to approximate e^(.1 * X)

that's useful for the natural logarithm 





Yes.... I did spend 14 hours figuring this out... and did I end up using it in an exam... YES!       AND DID I GET CALLED OUT FOR CHEATING??? 


no ... why would I?

Actually it's damn hard to multiply e by itself without a calculator