Possible Downtime and More Random Math
- needing 6-8 business days to make a simple transaction that can be made in less than half a second because of two little things I like to call: the internet and the 21st century
- sending two versions of a credit card within a week or two where activating the wrong one makes them both not work
- needing over a week to make and send a new credit card instead of just creating one on the spot in about 30 seconds as they easily could (just need a punch for the numbers and a magnetic strip writer)
- charging me an outrageous $54 annual fee for the privilege of carrying a piece of plastic around that didn’t work anyway
- charing a record high 30% interest rate on the credit card even though I’ve never missed a payment
- paying a record low 0.25% interest rate on my savings account, and even then only on amounts over $5,000; less than 1/3 of what RBC pays, and less than 1/4 of what HSBC pays
- working only 9:30am-4:00pm to avoid dealing with customers who have jobs
Anyway, hopefully the sites don’t go down, and here’s some more random math-ish stuff. Suppose you have a function in terms of its Taylor series about zero (it’s Maclauren series):
How can you find the square of the function? In hind sight, it should have been obvious, but it’s:
In fact, more generally, if we also have :
You can also calculate fairly simply:
Simply use forward substitution to solve for the values of .
It’s much harder to work out what non-integer powers of the Taylor series are, though. The pattern for seems too complex to figure out from 5 terms. What’d be really cool is to get the series for , since then most anything else would be pretty easy to figure out.