EXAMPLES OF LIMITS OF SEQUENCES

1

an = n/(n + 1) = 1 - 1/(n + 1)

as n increases , 1/(n + 1) approaches zero

an = (n2 - 1)/(n2 + n + 1) =

(1 - 1/n2 )/(1/n2 + 1/n + 1)

as n increases , 1/n and 1/ n2 approch zero

so that an approaches 1/1 = 1

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