Power sums refer to the sums of the powers of integers. For example, the power sum of the first n integers raised to a specific power k is expressed as S_k(n) = 1^k + 2^k + 3^k + ... + n^k . These sums can be calculated for various values of k and are often used in number theory and combinatorics. Mathematicians have developed formulas to compute power sums efficiently. The most famous of these is the Faulhaber's formula, which provides a way to express power sums in terms of Bernoulli numbers. Power sums have applications in areas such as algebra, calculus, and statistics.