<p>how do you find what each of the following series converge to?</p>
<p>(2n)/(n+3) (from 1 to infin.)</p>
<p>(-8)/((-3)^n) (from 1 to infin.)</p>
<p>1/(2^n) (from 0 to infin.)</p>
<p>looks like you can use the nth term test for #1 and geometric series test for #2 and #3.</p>
<p>Ah, I see that you are using the 2000 exam questions ;)</p>
<p>Well, the first one diverges, because the nth term test returns 2
the next 2 series are geometric series, so using this fact: a*sigma[r from 0 to inf] = a/(1- r), you do the following:</p>
<p>-8 * (-1/3)/(1 + 1/3) = 2
1 / (1 - 1/2) = 2</p>
<p>I don't think that the first one converges, since lim n-> infinity = 2.</p>
<p>The second one is a geometric series with a=-8 and r=-1/3. Evaluate [(8/3)/(1+1/3)] to get 2.</p>
<p>The third is another geometric series. [1/(1/2)] = 1.</p>
<p>The sum of an infinite geometric series is (first term)/(1-r).</p>
<p>thanks, i guess i was a bit taken aback by seeing 3 series in one problem :)</p>
<p>Oops, my third line should end in a 2.</p>