Let {xn} be a sequence of real numbers. Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer Hint: Use this theorem: If {xn} is bounded above, X = limsup(xn) if and only if For all & >0 and all M, there is n > M with X - ε < Xn

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Please use the theorem  to justify your answeer. Thanks

 

Let {xn} be a sequence of real numbers.
Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer
Hint: Use this theorem:
If {xn} is bounded above,
X = limsup(xn) if and only if
For all & >0 and all M, there is n > M with
X - ε < Xn
Transcribed Image Text:Let {xn} be a sequence of real numbers. Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer Hint: Use this theorem: If {xn} is bounded above, X = limsup(xn) if and only if For all & >0 and all M, there is n > M with X - ε < Xn
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