<p>If it was written incorrectly, tell us what the correct question is then!!</p>
<p>2/3<em>3/4</em>4/5<em>5/6</em>6/7<em>7/8</em>8/9*9/10 = 1/5 or 0.2</p>
<p>Compared to: </p>
<p>2/3<em>3/4</em>4/5<em>5/6</em>6/7<em>7/8</em>8/9<em>9/10</em>10/11<em>11/12</em>12/13<em>13/14</em>14/15*
15/16*16/17</p>
<p>=0.117</p>
<p>and</p>
<p>2/3<em>3/4</em>4/5<em>5/6</em>6/7<em>7/8</em>8/9<em>9/10</em>10/11<em>11/12</em>
12/13<em>13/14</em>14/15<em>15/16</em>16/17<em>17/18</em>18/19*
19/20<em>20/21</em>21/22<em>22/23</em>23/24*24/25</p>
<p>= 0.08</p>
<p>@bornagain
<a href=“http://i.imgur.com/E7Hz2.jpg[/url]”>http://i.imgur.com/E7Hz2.jpg</a></p>
![http://i.imgur.com/E7Hz2.jpg[/url]](http://i.imgur.com/E7Hz2.jpg%5B/url%5D){kind=link}
<p>I can’t believe we are still arguing this.</p>
<p>Start with n = 4.</p>
<p>2/3 * 3/4 * 4/5 = 2/5 = 0.4</p>
<p>Pick a large number, n = 1000.</p>
<p>Last two terms, [(n-1)/n]x[n/(n+1)], will give you a product of 0.998001998.</p>
<p>As n increases, the product of the last two terms gets closer to 1. That is true.</p>
<p>HOWEVER</p>
<p>We need to look at the product of all of the terms.</p>
<p>For n = 4, the entire product is 0.4</p>
<p>For n = 1000, the total product will certainly include the three terms of n = 4, so we will have:</p>
<p>0.4 * __________ * 0.998001998, where _________ represents all of the terms in between, which are all less than 1. Therefore, the __________ will have a value less than 1.</p>
<p>So we are multiplying 0.4 by two values less than 1 (the ________ and the 0.998001998), which will give a total product of less than 0.4</p>
<p>n = 4, the product is 0.4
n = 1000, the product is less than 0.4</p>
<p>It goes to zero.</p>
<p>[UPDATED x5] I’ll post here the answers everyone has listed so far in addition to some that I got:
Dice problem: 1/2
Shaded regions: 18
Multiplying fractions problem as x gets greater and greater: 0 (CONFIRMED!!!)
Simplifying polynomial problem: (W+X)^2-(Y+X)^2
Circle inside circle radius: 1/2x
Large rectangle: 1/2
Slope point problem (slope was like 4/5 and you had to find an equal point): (x+5, y+4)
X intercept: (9,0)
Tan of angle: >0
Geometric series (12, -4, 4/3, -4/9): 4/27
Smallest fraction problem [a is between 2 and 4, b is between 4 and 6, c is between 6 and 8, and d is between 8 and 10… you have to find the smallest number possible given (a/b)(c/d)]: .2 (something is off with the numbers i used in this example, but the concept is right)
Distance, midpoint problem [I don’t remember the exact numbers, so I will use my own in order to show the correct method: endpoint was (2,6), midpoint was (-1, −3)]: the x value of the other endpoint was −4
Principal’s salary: (94000) / (5(47)) or salary / (days worked per week * number of weeks)</p>
<p>For those still arguing about the fraction problem, read post #244. Never did it ask to only multiply the last two numbers… it asked for the product of the ENTIRE sequence. The whole 1 theory is that if you get a large value of n, the last two fractions will approach n. YES, that is right, but it’s NOT what the question was asking.</p>
<p>Yes, it was a horribly worded question, but 0 is the answer. End of discussion.</p>
<p>Here is another explanation if you’re not satisfied with that one. (the ------ line divides the numerator and the denominator of a fraction)</p>
<p>For n = 4:</p>
<h2>2<em>3</em>4</h2>
<p>3<em>4</em>5</p>
<p>The 3s and 4s cancel, leaving 2/5</p>
<p>For n = 7</p>
<h2>2<em>3</em>4<em>5</em>6*7</h2>
<p>3<em>4</em>5<em>6</em>7*8</p>
<p>All of the numbers cancel except 2 and 8, leaving 2/8.</p>
<p>THE EXPRESSION OF THE PRODUCT IS SIMPLE:</p>
<h2>2</h2>
<p>n+1</p>
<p>As n approaches infinity, the bottom approaches infinity and the product is zero.</p>
<p>for the 5th time, that’s the correct explanation if and only if you multiply each term together. HOWEVER, i finally remember it, what you have to do is multiply the 2 terms together and this creates what you are looking for. 2/3x 3/4= 0.5 (term one). 3/4 x 4/5= 0.6 (term two). 4/5 x 5/6= 0.66 etc. THE PROBLEM WAS NOT WRITTEN CORRECTLY ON THIS FORUM. EACH TERM WAS DERIVED VIA A MULTIPLICATION OF TWO PRODUCTS. YOU DO NOT MULTIPLY ALL OF THE TERMS TOGETHER.</p>
<p>I’m sticking with 1. It wasn’t asking you to multiply each consecutive term, it was basically asking you to find the limit of an equation as n approaches infinity.</p>
<p>*two numbers.</p>
<p>wccirl, I’ve had enough of you on every single one of these forums. Who are you to say that the discussion is closed? Because 80% of facebook thinks that 1+1+1+1+1+1x0 is 0, I guess then that must be the right answer, because majority rules, right? Just stop making authoritative statements and listen to other people. I remember what the question was, and I’m saying it.</p>
<p>ACT, Inc. already knows the answer to this question and your arguing won’t change anything. Move on to another question.</p>
<p>I think we covered most of the tricky ones, as far as I know.
I know I missed 1 for sure; it might be two if the answer really is 1.</p>
<p>Anyways, do act w/ writing scores come out at the same time as regular act scores?</p>
<p>yes, just often times minus the writing^</p>
<p>So you are saying that term one = (2/3)*(3/4), and so on.</p>
<p>What did you do with these terms? Did you multiply these terms together? Or did you simply look for the value of the last term when n is infinity?</p>
<p>Hey guys, I’m just joining the discussion. My credentials: 240 on the PSAT, 2370 SAT (800 math), and i rolled a 98% in Calc BC first semester. I’m pretty sure i got 60/60 on the math part today. (sincerely not trying to sound cocky)</p>
<p>Here are some of my answers:</p>
<p>Dice problem: 1/2
Shaded regions: 18
Multiplying fractions problem as x gets greater and greater: 0 (not confirmed)
Simplifying polynomial problem: (W+X)^2-(Y+X)^2
Circle inside circle radius: 1/2x
Large rectangle: 1/2
X intercept: (9,0)
multiplying fractions: if i understood the problem, it converges to 0.
sequence: 4/27
folding paper: 1/8th in
triangle side length: 8<x<14
which two have to be congruent: BX and DX</p>
<p>any other questions we should discuss?</p>
<p>Yeah, that’s what it was</p>
<p>@ugotserved834 you are so funny… we have proven why it equals 0, but you continue to argue that we are wrong without proving your point. If the question is worded wrong on here, tell us exactly what it said. It they only wanted you to multiply the last terms, why would they include the 2/3, 3/4 … part ??? That would be completely irrelevant.</p>
<p>Update: ugotserved, you can forward all of your ridiculous arguments to rollingdice now. Looking at his credentials, I would say that he is 100x more qualified than you to answer the question.</p>
<p>What was the answer to the line segment ratio one. It was like AB 2:3 what is ratio of AD. I put 2/5 I believe</p>
<p>I think that’s what I put as well.</p>
<p>@RollingDice
Why are you taking the ACT when you have a 2370 SAT score?</p>