<p>Somebody please tell me how to determine if a particular series converges or diverges. I know there are various tests for convergence but I've looked at examples of all of them and don't understand ANYTHING. </p>
<p>Also, does anyone know what the curve is for the Calculus BC exam?</p>
<p>Not sure what to say about the convergence tests, but the curve is leeeeeenient; somewhere around the high 60s-low 70s / 108 for a 5.</p>
<p>appass.com</p>
<p>Lagrange error is impossible. Nothing explains it clearly!</p>
<p>I’m also having trouble understanding the whole thing with Lagrange error bounds! Ugh. I am going to be in so much trouble tomorrow. My current school is tiny so there is only one other person taking this exam tomorrow besides me, and he isn’t motivated to study AT ALL so I’m basically on my own (i.e. no study buddy). I don’t know what to do… :(</p>
<p>Someone here will help I’m sure.</p>
<p>I’ll try to get you started.</p>
<p>Some series that you should memorize:</p>
<hr>
<p>1/n diverges</p>
<p>1/n^2 converges (or 1/n^anything where anything >=2)</p>
<p>(-1)^n / n converges</p>
<p>ar^n converges for any number a if abs(r) < 1 (“geometric”) and infinite sum = a / (1 - r)</p>
<hr>
<p>If the test doesn’t give you one of the above, you have to apply tests using the expression that is given for the nth term a_n.</p>
<p>1) if a_n goes to zero as n goes to infinity, go to step 2; otherwise, it diverges</p>
<p>2) try ratio test especially if you see factorials (e.g. n!) and/or powers (e.g., 5^n) and the terms are positive:</p>
<p>a) determine a<em>(n+1) / a</em>n, and find its limit as n -> infinity.</p>
<p>b) if answer < 1, converges; if answer > 1, diverges, if answer = 1, keep going.</p>
<p>3) is it alternating? I.e., a<em>n = (-1)^n b</em>n</p>
<p>If b<em>n > 0, b</em>n > b<em>(n+1), and b</em>n -> 0 as n->infinity, it converges.</p>
<p>4) if still no answer, you may have to try comparison test or integral test, not sure how often this occurs on AP exam</p>
<p>Hope this helps a little.</p>
<p>Learn the acronym: NNFEPL
It stands for what grows the fastest. Remember if something is top-heavy it automatically diverges. If it is bottom-heavy it MIGHT converge</p>
<p>basically, in order of growing fastest to slowest: n^n, n factorial, n^x, n^c (where c is a constant) and logn</p>
<p>Thank you both so much! Your posts just made my day (my life is pretty sad right now). I finally understand what’s going on. :)</p>