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Anreal

Let use "A". By the definition of the limit, we know that there exists N0 such that : "A"
This means that for "A"
Lets construct a new sequence Z=A. Since we know that both sequences XY and Y convergen. Theorem 1 states that sequence Z also convergen.
Notice that Z is actually N0-tail of Y, and since Z converges, theorem 2 states that Y converges as well

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