This has been fun. I think Mondays will become Sequences Day on my blog. Anyway, the follow are the first twenty terms of a sequence: 1, 1, 1, 2, 1, 3, 1, 4, 6, 1, 5, 10, 1, 6, 15, 20, 1, 7, 21, 35, . . . Same idea as the past two days. Describe the pattern of the sequence. Once you figure out the pattern, help me out with the behaviour of the mystical curve of best fit for this sequence at infinity. Is it infinity, or does it not exist? The derivative of the mystical curve of best fit, at infinity, like the function itself, is either infinite or does not exist. If you use a search engine, please don't submit it in the comments. If it hasn't been solved at the time, Thursday I'll post a hint in the comments section, and Friday, I'll post in the comments section the solution. If you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.
Tuesday, February 24, 2009
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7 comments:
Peter write something more interesting like how to convince a catholic what the bible says.
I wish I knew.
Here's one idea: Join Mormonism, through good works become a god, then regenerate the Catholic's heart, for, "Everyone who believes that Jesus is the Christ has been born of God" (1J. 5:1).
More seriously, I think Jesus responding to the Corban rule in Matthew 7:1-13 is really helpful.
Protestant: Mr. Catholic, if the Protestants can't have an infallible Bible without an infallible canon, how was the Old Testament infallible if there was no Roman Church to give an inspired canon?
Catholic: The Old Testament Church put their authority behind the canon of the Old Testament.
Protestant: So the Old Testament Church was infallible in its proclamations in the same way that the Church in Rome today is infallible in its proclamations. Is that right?
Catholic: Yes.
Protestant: So, in Matthew 7, when Jesus said the Old Testament Church was wrong for following the tradition they had set up, does that suggest they weren't infallible? Is the Roman Church then not actually infallible?
I'm not sure how a Catholic would respond.
Also, while I'm confident you've heard this before, but 2 Timothy 3:16, 17 is really helpful. "All Scripture is breathed out by God . . . that the man of God may be competent, equipped for every good work." For every good work, including teaching (v. 16). So, the Scriptures should teach them about Mary being eternally a virgin or emaculately conceived, or that the bishop of Rome is infallible, or that indulgences can take away sin, or that purgatory exists, or that you should pray to a saint (or, even ask a dead saint for prayer), or that they should bow down to the cross and to pictures of Mary.
If the man of God is to be equipped for the good work of teaching these things, it should be the God breathed Scriptures that equips him to do them.
Anyway, that's enough for now. I don't even know if you'll read this.
I hope KWTsui's not holding back.
The hint I'm going to give is to think combinations and permutations. But, while you're at it, don't over complicate it.
The sequence is each line of Pascal's triangle, up to the middle point but without the duplicates on the other side.
I have no idea how the curve/derivatives/etc. would work.
The curve goes to infinity and the derivatives (piecewise for each 1 to N section) are infinite at infinity. Overall the derivative is not defined.
I can't figure out a curve to fit the maximums (down the middle of the triangle) - but it's a rather steep function
Tristan is pretending to be mathy :p
T
I think that neither the limit at infinity, nor the limit of the derivative at infinity exist.
For a while I was thinking that since the infinitieth line of Pascal's triangle was of infinite length that maybe it would approach infinity, in which case, the limits of the function and its derivative at infinity would be infinite. But, upon further thinking, when you realize that real numbers (postive integers are real numbers) are always finite, there will always be oscillation. So neither limit exists.
Thanks for solving it, Jer.
the shape of the graph (n, nth term) is a zigzag. Like the spines on the back of a dragon.
Each spine gets steeper and steeper until the slope becomes infinity at infinity.
If you graph the maximums (the peaks of the spines or the line straight down the middle of the triangle), the general curve shoots vertical quite quickly.
That is why I said it's piecewise infinitive - but undefined as a whole
T
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