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sequence in which sum of terms equals product of the same terms

Source: Romanian District Olympiad 2012, Grade XI, Problem 1

October 9, 2018
Sequenceslimitreal analysis

Problem Statement

Consider the sequence (xn)n≥1 \left( x_n \right)_{n\ge 1} having x1>1 x_1>1 and satisfying the equation x_1+x_2+\cdots +x_{n+1} =x_1x_2\cdots x_{n+1} , \forall n\in\mathbb{N} . Show that this sequence is convergent and find its limit.
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