Explanation via examples! (Please include an example next time so we don't waste each other's time talking about stuff that's not the question

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街に行き、買い物をします。
Verb stem by itself functions like て form and is a conjunction. It is more or less "and". "I go town and do shopping."
座りたまえ!
たまえ is a pretty rare way of giving an imperative or order. "Sit down!" If you want a good example, listen to the Führer speak in Fullmetal Alchemist - he uses it all the time.