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Analysis of an infinite sequence

Assignment

Now we will expand our investigation to determine the sum of the infinite sequence tn, where
t0=1,t1=(xlna)1,t2=(xlna)22x1,t3=(xlna)33x2x1,…

Define Tn(a,x) as the sum of the first n terms, for various values of a and x.
e.g. T9(2,9) is the sum of the first nine terms when a=2 and x=5.

Let a=2. Calculate T9(2,x) for various positive values of x. Using technology, plot the relation between T9(2,x) and x. Describe what you notice from your plot.

Let a=3. Calculate T9(3,x) for various positive values of x. Using technology, plot the relation between T9(3,x) and x. Describe what you notice from your plot.
Continue with this analysis to find the general statement for Tn(a,x) as n approaches ∞.
Test the validity of the general statement with other values of a and x.
Discuss the scope and/or limitations of the general statement.
Explain how you arrived at the general statement....