sum1Ci

In mathematics and computer science, sum1Ci is a shorthand notation used to denote the sum of the integers i from 1 to C. It appears in various texts and code as a compact representation of an arithmetic series.

Formally, sum1Ci equals 1 + 2 + ... + C, and is known as the Cth triangular number. The closed-form expression for this sum is C(C + 1)/2 for any positive integer C. This compact formula allows the sum to be computed in constant time without iteration.

In many contexts, sum1Ci is not a standard symbol but rather a descriptive alias or a function name in code. The conventional mathematical notation uses the summation symbol Σ with limits i = 1 to C. When C is large, the closed-form expression is preferred to avoid looping through all terms.

Properties associated with sum1Ci include its strict increase as C grows and its size on the order of C^2/2. It is also the Cth triangular number and represents the number of dots in a triangular arrangement of side length C. This concept frequently appears in combinatorics, number theory, and algorithm analysis.

Example: for C = 5, sum1Ci = 1 + 2 + 3 + 4 + 5 = 15, which equals 5 × 6 / 2. In programming, care should be taken to prevent overflow for large C by using appropriate integer types or arbitrary-precision arithmetic.