a(n) := (x^n)/n
x from R
with n approaching infinity, in the above sequence, the dominant term is the numerator? or because x is not a variable the dominant part is the denominator?
The convergence/divergence of $\displaystyle \frac{x^n}{n}$ depends on the value of $\displaystyle x$.
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Change the 2 to .2 then change it to -2. See the difference.