A short thread about the limit of the infinite sum
1 + (1-n) + (1-n)^2 + (1-n)^3 + ...
assuming that n is positive and less than two:

(1/n)

Furthermore, the derivative (with respect to n) of the natural log of n^2 has the property that it can be expressed as a constant times a (negative) power of n, making it a rather trivial example of a finite Laurent series. In fact, it's exactly

(2/n)

If you take an entry of the Schläfli matrix corresponding to a Coxeter diagram edge labelled n, multiply by -2, and apply the inverse cosine function, you get an expression involving a famous transcendental constant. If you approximate it by an integer, what results is

(3/n)

Consider the set of Gaussian integers whose modulus is one. Take the quotient of this set with respect to any group action of the group ℤ_n. Now compute the cardinality of the resulting groupoid:

(4/n)

In conclusion, even though it's technically undefined for one particular value of n, it can easily be shown that the limit as that point is approached attains the same (constant) value as the function's output elsewhere. What function am I talking about?

(n/n)