Is there a limit in this progression? 1.1 + 2.1 + 2 + 3.1 + 2 + 3 + 4

Is there a limit in this progression? 1.1 + 2.1 + 2 + 3.1 + 2 + 3 + 4

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Infinite? and how to demostrate it?

which progression is the sequence in ?

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