# A simple problem

Calculus Level 4

Denote $\displaystyle f(x) = \sum _{ n=1 }^{ \infty }{ { T }_{ n }{ x }^{ n } }$ where domain of $f(x)$ are all values of $x$ where the summation converges, and ${T}_{n}$ is the $n^{\text{th}}$ term of some sequence.

We define ${S}_{n} = {T}_{1}+{T}_{2}+ .... +T_{n}$

And $\displaystyle g(x) = \sum _{ n=1 }^{ \infty }{ { S }_{ n }{ x }^{ n } }$ with domain of $g(x)$ are all values where this summation converges.

Lastly, denote $h(x) = \dfrac { f(x) }{ g(x) }$, domain of $h(x)$ is the intersection of domain of $f(x),g(x)$ and values where $g(x) \neq 0$

Then find $x+h(x)$ in its domain.

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