2011 SAC Test / Mathematician Study Guide?

[Jeremy2012x]

If someone could explain these two problems that have to do with the 2011 - 2012 Special Emphasis concept

18) Determine the sum of the infinite series 1 + 1 + 1/2 + 1/6 + 1/24 + . . . (nearest thousandth)

23) Find k given the sequence 2,3,10,15,26,k,50,63,82

Also, #2 on the SAC notes that follow the test found on the official UIL website
http://www.uiltexas.org/files/academics ... le2012.pdf

Lastly, would you guys be interested in creating a study guide gpt the mathematicians? For example, we could each post one or two sentences about whichever mathematician someone requests (specifically posting info that has appeared on previous tests)

[nsguy1350]

18. Infinite series for e!!!
Sum of the reciprocals of factorials is e ~ 2.718. This is a MUST-KNOW!!! :D

23. During the SAC, I was one of two to figure out without the "gap" technique, where you find gaps between numbers to find a pattern. The sequence is [unparseable or potentially dangerous latex formula].

Yes, I'd like to create a mathematician study guide. We could get one guy to start, everyone can post, and then the guy will edit his previous post by adding info that people mention.

EDIT: #2 can be found by using the fact that the cycle repeats every 8 numbers. 2012 mod 8 = 4, so just find the fourth number, which, if my memory is correct, is in column D.

[Jeremy2012x]

Thanks a ton! For 23, however, how did you derive the pattern simply by looking at it? Does it just take a while to get used to identifying these patterns?

[nsguy1350]

I don't really know... it just hit me. I usually check for arithmetic/geometric sequences, then Fibonacci-characteristic, then patterns such as slight alterations of squares and things. Really a hit-or-miss type of sequence. The "gap" technique is useful, if you get stuck. However, it's not as elegant as it could be.
Now, it was not immediate. It took a few seconds, at the least, of deep thought.

[Salvadoramerican]

wow that smart i would have done the exact same thing with the aritmitic sequence