Infinite Summation: Define Tn & Find x,a Relationship

[krayzee]

Homework Statement

Define T_n as the sum of the first n terms, for various values of a and x, e.g. T₉(2,5) is the sume of the first nine terms when a = 2 and x = 5.

The first n terms are 0-10, including both 0 and 10.

Homework Equations

T₀=1, T₁= (xlna)¹/1, T₂= (xlna)²/2!, T₃= (xlna)³/3!... T_n = (xlna)ⁿ/n!

The Attempt at a Solution

Using a graphing calculator, seq(xlna)^n/n!,n,0,10)

The relationship between x and a is: n --> infinity, S_n --> ax, S_n represents the sum of n.

 

[rock.freak667]

I am not too sure what the question is but this seems like it might help


$$e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+... = \sum_{n=0} ^{\infty} \frac{x^n}{n!}$$