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Binomial theorem formulas
7 formulas for Binomial theorem, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Expansion | (a + b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ, r = 0…n | |
| General term | Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ | |
| Middle term (n even) | T(n/2 + 1) | |
| Middle terms (n odd) | T((n+1)/2) and T((n+3)/2) | |
| Sum of coefficients | ⁿC₀ + ⁿC₁ + … + ⁿCₙ = 2ⁿ | |
| Odd = even coefficients | ⁿC₀ + ⁿC₂ + … = ⁿC₁ + ⁿC₃ + … = 2ⁿ⁻¹ | |
| Binomial series | (1 + x)ⁿ = 1 + nx + n(n−1)x²/2! + … | |x| < 1 for any real n |
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