How to use the binomial theorem coefficient calculator
Find the kth term of (a + b)^n. Enter power n, term index k, a, b in the fields above; the binomial coefficient, term value are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “expand binomial”, “pascal triangle row”, “term of expansion”, “calculate binomial theorem coefficient”, “find binomial coefficient”.
Formula
Variables
- n — Power n
- k — Term index k
- a — a
- b — b
Worked example
With power n = 8, term index k = 3, a = 2, b = 1, the calculator gives binomial coefficient ≈ 56; term value ≈ 1,792.
Frequently asked questions
What is the binomial theorem coefficient calculator used for?
Find the kth term of (a + b)^n. It helps with questions such as “expand binomial”, “pascal triangle row”, “term of expansion”.
What is the formula for the binomial theorem coefficient calculation?
Binomial coefficient = nCr(n,k). Term value = [Binomial coefficient] × a^(n-k) × b^k. Here n is power n, k is term index k, a is a, b is b.
What inputs do I need for the binomial theorem coefficient calculator?
You need power n, term index k, a, b. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the binomial theorem coefficient calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the binomial theorem coefficient result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.