# 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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