Power Series Calculator
x value
Number of terms
A power series represents a function as an infinite sum of terms involving powers of x. They are used to approximate functions like eˣ, sin(x), and cos(x) with polynomials.
- 1eˣ = 1 + x + x²/2! + x³/3! + ...
- 2sin(x) = x − x³/3! + x⁵/5! − ...
- 3cos(x) = 1 − x²/2! + x⁴/4! − ...
- 4More terms = better approximation
eˣ at x=1, 5 terms=1+1+0.5+0.167+0.042 ≈ 2.708 (actual: 2.718)
sin(π/6), 4 terms=≈ 0.5 (exact)
| Terms | Sum | Error vs e |
|---|---|---|
| 2 | 2.000 | 26.4% |
| 4 | 2.667 | 1.9% |
| 6 | 2.718 | 0.006% |
| 10 | 2.71828 | < 0.00001% |
References
🔒
100% Gratis
Ingen registrering
✓
Korrekt
Verifierade formler
⚡
Omedelbar
Resultat direkt
📱
Mobilanpassad
Alla enheter