Let n be a positive integer. Consider the binomial expansion of n^k for any positive integer k: n^k = (n-1)^k + Σ(i=1 to k) (-1)^(i+1) * (k choose i) * n^(k-i) Conjecture For any integer k > 2, the ...

Using a relationship derived from a special case of DeMoivre's Theorem, we can express the sine and cosine functions as infinite series of generalized binomial coefficients. We will derive these ...