Let a be a single-digit positive integer. Let n be another positive integer that adjusts itself so that the unit's place digits of n and an + 1 are the same. Find the sum of all possible values of a.
For some positive integer k both 4^k and 5^k start with the same digit x in base 10 i.e. 4^k = x..... 5^k = x..... What is the sum of all possible values of x.
Let Ln denote the arc length of the curve x^2n + y^2n = 1 where n is a positive integer. Find Lim (n->∞) Ln
