Consider the function \[S_n(x) = 1 + \frac{2}{1+x} + \left( \frac{2}{1+x} \right)^2 + \dots + \left(

Question

Consider the function $$S_n(x) = 1 + \frac{2}{1+x} + \left( \frac{2}{1+x} \right)^2 + \dots + \left( \frac{2}{1+x} \right)^n, \quad x \neq -1.$$ Determine the set of values of $x$ for which the sum to infinity $S(x)$ exists.

Accepted Answer

x 1

Sum to infinity with undetermined range

Sum to infinity with undetermined range

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