ClarityHow to use this tool
- Enter row n (top row is 0).
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
Begin with coefficient one and update C(n,k+1)=C(n,k)×(n−k)/(k+1). Each exact integer is a coefficient of (a+b)^n.
Using row n (top row is 0) = 10, the result is 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
The row is symmetric, starts and ends in one, and its coefficients sum to 2ⁿ. These properties provide quick checks for indexing mistakes.
What to keep in mind
Top row is row zero. Output contains n+1 integer coefficients, with n limited to 500. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.
Common questions
How can I verify a row?
The row is symmetric, starts and ends in one, and its coefficients sum to 2ⁿ. These properties provide quick checks for indexing mistakes.
How can I check the result?
Begin with coefficient one and update C(n,k+1)=C(n,k)×(n−k)/(k+1). Each exact integer is a coefficient of (a+b)^n. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.