Value-at-Risk Theory and Practice

The first advanced book on value-at-risk

Chapter 2, Page 64
Exercise 3

Construct the Taylor series expansion for the function log(1 + x) about the point = 0.

 

Solution

We construct the Taylor series as

[s1]

We have
f(x) = log(1 + x) [s2]
   
[s3]
   
[s4]
   
[s5]

More generally

[s6]

Valuing [s2] through [s6] at = 0 and substituting the results into [s1], we obtain the Taylor series

[s7]

 
 

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