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 ...

What are Sequence and Series? A sequence is a structured arrangement of numbers, where each number is called a term. Typically, terms in a sequence are denoted as ai or an, with the index letter i or ...