L IMITS OF I NFINITE S EQUENCES Ch. 13 (4). What happens to each term as n gets very large?

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Presentation transcript:

L IMITS OF I NFINITE S EQUENCES Ch. 13 (4)

What happens to each term as n gets very large?

Theorem: If |r|<1, then (sometimes it helps to put in very, very large numbers for n) Example:

F IND THE FOLLOWING L IMITS (H INT : P UT VERY !!! LARGE NUMBERS IN FOR N )

H INTS FOR FINDING 1. If the degree of the numerator is less than the degree of the denominator, lim = 0 2. If the degree of the numerator is greater than the degree of the denominator, lim = DNE, 3. If the degree of the numerator = degree of denominator, the limit is the ratio of the lead coefficients.

F IND THE FOLLOWING L IMITS (H INT : U SE THE SHORT CUTS !!!