Calculate the sum of a polynomial sequence over a range of indices.
Summation Range & Function
Function: Ai³ + Bi² + Ci + D
Total Sum
55
Σ f(i)
Calculated by iterating through the range and evaluating the polynomial.
Number of Terms10
Σ i=1 to 10
Partial Expansion
1 + 2 + 3 + 4 + ... + 10
About this calculator
What is Summation?
Summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. The uppercase Greek letter Sigma (Σ) is used as a symbolic shorthand for the sum of many terms.
💡
Pro Tips
The start index must be less than or equal to the end index.
Polynomial summation can also be solved using closed-form identities for i, i², and i³.
Sigma notation is widely used in physics, statistics, and computer science algorithms.
!
Fun Facts
"The symbol Σ was introduced by Leonhard Euler in 1755."
"The sum of the first 100 integers is 5,050 (famously calculated by a young Gauss)."
"Infinite summations are called 'series' and can converge to a finite value."
