Infinite Series Expansion Of E X

Complete solution before starting this problem note that the taylor series expansion of any function about the point c 0 is the same as finding its maclaurin series expansion.

Infinite series expansion of e x. This leaves the terms x 0 n in the numerator and n. How it can find the logarithm of any positive number you give it. How a calculator can give you the value of sine or cos or cot of any angle. It should be evident that you can consider the product tag 1 color maroon bigl 1 x frac x 2 2 frac x 3 3 frac x 4 4 frac x 5 5 frac x 6 6 bigr color darkgreen bigl 1 frac x 2 2 frac x 4 4 frac x 6 6.

Find the taylor series expansion for e x when x is zero and determine its radius of convergence. The mathematical constant e can be represented in a variety of ways as a real number since e is an irrational number see proof that e is irrational it cannot be represented as the quotient of two integers but it can be represented as a continued fraction using calculus e may also be represented as an infinite series infinite product or other sort of limit of a sequence. In the denominator for each term in the infinite sum. How it can give you the square root or cube root or 4th root of any positive number.