SO THIS IS OUR QUEST:

(1)   To understand the meaning of addition of infinitely many numbers which are getting infinitely small.

(2)   To get formulas for our most important functions as ``infinitely long polynomials'' (Taylor series).

(3)   To be able to use such formulas for practical tasks, like estimating function values or solving differential equations.

Exercise 2:

If f(x) = e^x and and T_n(x) = 1 + x + x² / 2! + x³ / 3! + ... + xⁿ/ n! ,

show that f⁽ⁿ⁾(0) = 1 = T_n⁽ⁿ⁾(0).