<p>Okay I was doing this series question in Collegeboard and here is what I got:</p>
<p>2x*lim (n approaches infinity) |(n+1)/(n+2)|</p>
<p>Isn’t |(n+1)/(n+2)| approaching 0 so whole product = 0?</p>
<p>I think the quantity is approaching 1…</p>
<p>It approaches 1, not zero. You look at the leading terms, in other words, it becomes lim(n/n) which is 1.</p>
<p>AHHH That was stupid. It’s clear that if I put n = 9, 99, 999… I get 0.99999999 etc.</p>
<p>Hmm let’s say I have (n-2)/(n+5). How will I know what this approaches (as n gets bigger)?</p>
<p>That’d still be 1. Take a look at the leading coefficients- n/n. anything with the same power can be reduced. n/n -> 1. 2n/n -> 2.</p>