Maclaurin Series vs Maclaurin Polynomial

Maclaurin series - is an infinite sum
Maclaurin polynomial - is a finite sum

Maclaurin Series/Polynomial - Definitions

Power Series Centered at Zero

Taylor Series/Polynomial Centered at Zero

A Maclaurin series is a power series centered at zero (i.e. 𝑐 = 0)

When all coefficients are equal 𝑎_𝑖 are equal it is a geometric series

A Maclaurin series/polynomial is a polynomial centered at zero

power series form
compact sigma form

where:

𝑛! denotes the factorial of 𝑛
𝑓^(𝑛)(0) denotes the 𝑛^𝑡ℎ derivative of 𝑓 evaluated at the point 0