Power Series Calculator
Calculate power series (Taylor/Maclaurin series) expansions for exp, sin, cos, ln, and more.
Function
Series Formula:
e^x = ∑ x^n / n!
Radius of convergence: ∞
Partial Sum (10 terms)
2.7182815256
Exact Value
2.7182818285
Absolute Error
3.0289e-7
Relative Error
0.000011%
Individual Terms
n=0:1.000000e+0
n=1:1.000000e+0
n=2:5.000000e-1
n=3:1.666667e-1
n=4:4.166667e-2
n=5:8.333333e-3
n=6:1.388889e-3
n=7:1.984127e-4
n=8:2.480159e-5
n=9:2.755732e-6
Common Power Series
e^x
= 1 + x + x²/2! + x³/3! + ...
sin(x)
= x - x³/3! + x⁵/5! - ...
cos(x)
= 1 - x²/2! + x⁴/4! - ...