The limit of the expression (1 + 1/n^2)(7/n + 1) as n approaches infinity is evaluated. The correct approach involves recognizing that as n becomes infinitely large, the terms 1/n^2 and 7/n approach zero. Therefore, the limit simplifies to 7 * 1, resulting in a limit that exists and equals 7. The initial assertion that the limit does not exist is incorrect.
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No. Don't multiply the two factors. Each one has a limit that is readily obtainable. As n gets large without bound, what happens to 1/n2? What happens to 1 + 1/n2? What happens to 7/n? What happens to 7/n + 1?naspek said:Homework Statement
lim... (1 + 1/n^2)(7/n+1)
n->infinity
The Attempt at a Solution
lim... (1 + 1/n^2)(7/n+1)
n->infinity
= (7/n + 1) + (7/n^3 + n^2)
bring out 7 because constant..
7lim... (1/n + 1) + (1/n^3 + n^2)
n->infinity
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7lim... (n^2 + n + 1) / (n^3 + 2n^2 +n)
n->infinity
limit does not exist.. am i correct?