<p>Tell me if the following diverge or converges</p>
<ol>
<li>ln(4n)/n</li>
<li>ne^(7n)</li>
<li>10/(nln(4n)^5))</li>
<li>(n+2)/(-4^n)</li>
<li>ne^(-7n)</li>
</ol>
<p>sum from 1 to infinity</p>
<ol>
<li>diverges; p-series test.</li>
<li>diverges, ratio test</li>
<li>diverges; limit-comparison test</li>
<li>converges; ratio test
5.converges; ratio test</li>
</ol>
<p>This is my answer, but I am doubtful of 3.</p>
<p>which of the above wouldnt it be possible to apply the integral test? is #2 the only one that you wouldnt be able to apply the integral test because it is increasing?</p>
<p>yeah, you can’t apply integral test on 2 since, like you said, it is increasing.</p>
<p>grr, my online practice homework for the AP isnt taking the ansewers.</p>
<p>heres the question for the series above.
Test each of the following series for convergence by the Integral Test. If the Integral Test can be applied to the series, enter CONV if it converges or DIV if it diverges. If the integral test cannot be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the Integral Test cannot be applied to it, then you must enter NA rather than CONV.) </p>
<p>i put
- div
- na
- div
- conv
- conv</p>
<p>for 4. the problem is actually (n+2)/((-4)^n), not sure if that would make a difference</p>
<p>^either way, i still i got convergent.</p>
<ol>
<li><p>ln(4n)/n
Diverges (integral test)</p></li>
<li><p>ne^(7n)
Diverges (nth term)</p></li>
<li><p>10/(nln(4n)^5))
Converges (integral test)</p></li>
<li><p>(n+2)/((-4)^n)
Converges (alternating series)</p></li>
<li><p>ne^(-7n)
Converges (integral test)</p></li>
</ol>