September 2020

Binomial Theorem Corollaries

Here are some simple proofs based on the binomial theorem. They also demonstrate how amazing mathematical proofs can be. 1. The hockey stick identity By the formula for the sum of a geometric series, \(\frac{(1+r)^{n+1}-1}{(1+r)-1}=\displaystyle\sum_{i=0}^n (1+r)^i\). Now expanding both sides by the binomial theorem and simplifying, $$\displaystyle\sum_{i=0}^n \binom{n+1}{i+1}r^i=\displaystyle\sum_{i=0}^n \displaystyle\sum_{j=0}^i \binom{i}{j}r^j$$ Now rearrange the sum on […]

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Some Math Jokes

A \(K_5\) graph walks into a bar. A \(K_4\) graph follows it. The bartender points to the \(K_4\) and says, “Sorry, we don’t serve minors here.” A man goes to a yard sale. He sees a nice mug. He asks the seller, “How much does this cost?” The seller replies, “\$2” He then eyes a

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What is a Log?

Scientist: Log is the basis of the pH and Richter scales Mathematician: Log is the integral of $\frac{1}{x}$ Programmer: A log is generated by a program to help in debugging Lumberjack: Logs are what keep my buisness running IT professor: There are two types of log: log in and log out Camper: Logs are used

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