Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...

Transactions of the American Mathematical Society, Vol. 359, No. 3 (Mar., 2007), pp. 1161-1189 (29 pages) We consider sums of the form $\sum_{j=0}^{n-1}F_{1}(a_{1}n+b ...

Number sequences are sets of numbers that follow a pattern or a rule. Each number in a sequence is called a term. There are some special sequences that you should recognise. The most important of ...