<p>I have a doubt with mc #38 in P.R. BC practice test 1</p>
<p>IF f(x) = summation (0 to infinity) (cos^2 (x))^k, then f(pi/4) is</p>
<p>Why is 1 instead of 2?</p>
<p>a=1
r=(cos^2 (pi/4))=.5</p>
<p>S=1/(1-.5)=2</p>
<p>HOWEVER, the solution said: a=1/2, howcome??</p>
<p>Please help</p>
<p>I have no idea.... good question.</p>
<p>bump</p>
<p>Firstly, that isn't a geometric series. I'm having some problems understanding your notation, so I'll get back to you soon, but you can only use the a/1-r thing on a geometric series.</p>
<p>i thought it was a geometric series since cos^2 (x) is raised to the k</p>
<p>TO: eponymous</p>
<p>That's a Geometric series.
For this question, it use "k" instead of "n".
and k is from 0 to infinity.</p>
<p>Since, (cos^2 (pi/4))=.5 which is less than between -1 to 1 and non-zero.
So, Geometric series is applying.</p>
<p>Basically, would PR has a wrong answer?</p>
<p>i think ur solution's right, cuz (1/2)^0=1</p>
<p>no idea wut PR did over there</p>
<p>TO: toothpickforest</p>
<p>If we are correct, basically, PR mistake is taking a=1 instead of a=.5, and PR's method is long and dumpy.
However, if we are wrong, I should learn from PR tonight.</p>
<p>hahah..i kinda gave up on pr after finding a ton of errors in the programmin book. some of the errors were just ridiculous: the answer is D. explanation: since blah blah blah, we can eliminate choices A and D...wth???</p>
<p>btw i checked w/ a calculator, the answer's 2 :)</p>
<p>TO: toothpickforest</p>
<p>Using TI-89?
haha</p>
<p>I think PR is wrong because they used the wrong formula. THey tell you not to do a<em>r/(1-r) but then do it anyway. Here's what PR is saying: the formula is a</em>(r/(1-r)). a=1, as you all said, but there is the r in the r/(1-r) part. r=1/2 (cos^2(pi/4) = (sq(2)/2)^2 = 2/4 = 1/2). Therefore, you get 1/2 * 1/(1-cos^2x) or 1/2 * 1/sin^2x, you plug in pi/4 for x, and you're done.</p>
<p>Keep in mind, though, that PR used the wrong formula after telling us not to.
("Notice that if the series went from one to infinity, instead of zero to infinity, then the formula would be a(r/(1-r)). Be careful you memorize the correct formula"). Yeah, PR...be careful... :p</p>