I recently encountered this beautiful problem in Crux Magazine (OC726) that initially seemed quite intimidating, but turned out to have a surprisingly elegant solution once you find the right perspective. Usually in school we are asked to integrate explicit functions. Is it possible to integrate implicit functions? For instance, suppose we know that g(x) is […]
Here’s an interesting problem related to voting and ballot counts:
Suppose A and B win p and q votes respectively in an election with p > q. While counting the ballots, what is the probability that A always remains ahead of B throughout the count?
Andre’s reflection trick solves this problem.
In this post, we will define binomial coefficients using integration of complex valued functions and prove high school identities using integration methods. 12th standard students who are learning calculus should be able to follow this post. You can consider this as a practice in integration theory. I usually call such fun extras as JEE side
Introduction A polynomial in one variable $x$ with real coefficients is an expression that can be made by adding, multiplying, subtracting real numbers and the variable $x$. For instance, consider the expression $x^2 + 3x +2$, which is simply the wordy algorithm Think of a number, square it and add it to three times to
