totalSum

Totalsum is the sum of all elements in a finite collection of numbers, or the sum of all terms in a sequence. In mathematics, the total of a finite sequence a1, ..., an is written S = ∑_{i=1}^n a_i. The concept extends to infinite series S = ∑_{i=1}^∞ a_i, where the total exists only if the sequence of partial sums s_N = ∑_{i=1}^N a_i converges to a finite limit; if it does not converge, the total is said to diverge.

For finite sums, the order of addition does not affect the result because addition is associative and commutative. In the context of infinite series, convergence depends on the terms, and rearrangements can influence the sum for some conditionally convergent series.

Examples: If a = [3, 5, -2], then S = 3 + 5 − 2 = 6. Partial sums are 3, 8, 6. The total of a data set is often used to compute the mean or to compare totals across datasets.

In applications, totals are used in statistics, finance, and programming. A related concept is the cumulative or prefix sum, where running totals s_k = ∑_{i=1}^k a_i are maintained for range queries.

Numerical aspects: computing a total in floating point can introduce rounding errors; compensated summation methods (such as Kahan summation) reduce such errors. Time complexity is O(n) with O(1) extra space.