# Does an infinite series with an unbounded number of terms with the same value converge

Suppose one has an infinite series of positive reals. And suppose that there are an infinite number of sets of terms $S_n$ which take the same value. That is:

$S_1 = \{ a_{1,1}, a_{1,2},...,a_{1,m}\}$, $a_{1,m} = c_1$

$S_2 = \{ a_{2,1}, a_{2,2},...,a_{2,m}\}$, $a_{2,m} = c_2$

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