Feel smart. More math help. BlackSix, I'm looking at you.

[Kurt_]

Well, I'm getting better at working through problems on my own, but every now and then I need some help with them. The next math class is a review class, but it's also Friday afternoon. With the test being Friday night, I don't plan on waiting until then with some of these questions.

http://www.math.mcmaster.ca/childsa/1z04/sample3.pdf

All question can be found there.

Here's the one's I'm having trouble with (expect updates):

1st Sample Test #9:

If the sequence is zero (line along the x-axis), why does it converge with a limit of zero?

1ST #11:

Through logic, I can estimate the sum is less than one, but that still leaves me with answers C and D. To be honest, I'm not sure where to begin. It's not a telescoping sum, and it is divergent so most tests I know won't work on it.

[Black Six]

For #9 I believe the answer is (b). (i) is going to oscillate between +1 and -1 and never converge, ergo it's divergent. In (ii), sin(n*pi) is always 0, so every element in the sequence will be zero, hence it will converge to zero.

I'm gonna have to sleep on #11. Series were never my strong suite.

[Black Six]

Yeah, nothing's coming to me. If I get some time this weekend I'll try to refresh myself on things, but if anyone else has an idea by all means lend a hand!

[Kurt_]

Well the test was tonight.

#9:

That's just how straight lines roll.

#11:

It can be put into the form of a geometric series.

(sinx/3)^n.

Recall:

Geometric Series = First Term / 1 - r
where r is the base to the exponent n +/- a number

aka a/(1-r)

The series can be written as:

(sinx/3)(sinx/3)^n-1

Given that, the first term is sinx/3.
r is also (sinx/3)

so...

sinx/3 / 1 - sinx/3 all multiplied by 3 will give you

sinx / 3 - sinx.


I think I did very poorly on that test. My best mark yet, no doubt!

[Black Six]

Yeah, series suck. Once you get away from that I could probably be more helpful again. It's also been like three years since I've had to use them (take comfort in that, unless you're a math major they're pretty much useless, unlike other parts of calculus).

[Kurt_]

Thanks for all the help!

I probably won't need it again until next semester (More than likely sometime in early February) as exams are soon and that's when the next test will be. But I heard next semester math is geometry and discrete, which I adore.