Suppose {an} and {bn} are sequences, and an = bn for all n ≥ 1000, but

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Suppose {an} and {bn} are sequences, and an = bn for all n ≥ 1000, but an ≠ bn for n < 1000. Is it true that lim n → ∞ an = lim n → ∞ bn? True False

Please show and explain your work. Thanks

Suppose

{a_{n}}

and

{b_{n}}

are sequences, and

a_{n} = b_{n}

for all

n \geq 1000

, but

a_{n} \neq b_{n}

for

n < 1000

. Is it true that

lim_{n \to \infty} a_{n} = lim_{n \to \infty} b_{n}

?
True
False

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