LaTeX
\sum_{k=1}^{n}k=\frac{n(n+1)}{2}Variables
- n: positive integer upper limit
- k: summation index
How to use this formula
Calculates the total of the integers from one through n.
Important notes
- The identity can be proved by pairing terms from opposite ends.
- For n = 0 the empty sum is zero.
Quick example
For n = 10, the sum is 10×11÷2 = 55.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The identity can be proved by pairing terms from opposite ends.
- For the Sum of the First n Positive Integers, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Sum of the First n Positive Integers, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- Confirm the finite-set, indexing, ordering, and counting conventions assumed by the expression.
Worked example
For n = 10, the sum is 10×11÷2 = 55.
Common mistakes
- When copying Sum of the First n Positive Integers, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Sum of the First n Positive Integers with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Sum of the First n Positive Integers in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\sum_{k=1}^{n}k=\frac{n(n+1)}{2}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Sum of the First n Positive Integers used for?
Calculates the total of the integers from one through n.
Can I copy this formula as LaTeX?
Yes. Copy \sum_{k=1}^{n}k=\frac{n(n+1)}{2} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.