factorials, square roots, and infinite series

This is a discussion on factorials, square roots, and infinite series within the A Brief History of Cprogramming.com forums, part of the Community Boards category; a few math questions in the binomial expansion theroem equation, basically: Code: (a+b)! -------- a! * b! where a+b is ...

  1. #1
    Just because ygfperson's Avatar
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    factorials, square roots, and infinite series

    a few math questions
    in the binomial expansion theroem equation, basically:
    Code:
    (a+b)!
    --------
    a! * b!
    where a+b is the exponent to multiply out a (x+y) binormial, and b+1 is the b'th element in that line in pascal's triangle

    how is that equation derived?
    *****
    is there a way to get a square root of a non-square number without a bunch of trial and error?
    *****
    in an infinite geometric series, the equation for the sum is:
    Code:
     a
    ---
    1-r
    where r is between 1 and -1, and a is the first element. how is this equation derived? i can only get this far:
    Code:
    sum = a + a*r + a*r^2 + a*r^3 ...
        = a(1 + r + r^2 + r^3 ...)

  2. #2
    ¡Amo fútbol!
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    A) Is this calc, cause this **** is crazy.

    B) How old are you?

  3. #3
    Just because ygfperson's Avatar
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    a) pre-calc
    b) 17

    on the first question, i just want to know how ppl derived the binomial expansion theorem.

    oh, and fyi, this isn't any kind of homework... i'm just curious
    Last edited by ygfperson; 06-04-2002 at 09:03 PM.

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    Prisoner of my own mind
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    Non perfect squares have irrational roots so it depends on how accurate you want to be and if you're after quick easy calculations for a few decimal places on paper or an algorithm for as many as you can be bothered or you want a PC to use, remembering of course the limit of the finite number set on a PC.

    A reasonable approximation for a few decimal places or so for numbers greater > 1 follows presented as an example for simplicity.

    What is the square root of 27?

    Now 25^1/2 = 5, and 36^1/2 = 6

    let 5+x = 27^1/2 where x is less than 1.
    27 = (5+x)^1/2
    27 = 25 +10x +x^2
    Since x < 1, x^2 is "small" so ignore it.
    27 ~ 25 + 10x
    x ~ 0.2

    Giving 27^1/2 = 5.2
    5.2^2 = 27.04

    Algorithm-wise, try looking at math libraries. I only one I looked at was for the sine function and I can't remember if it were just trig functions or a more general maths algorithms, or the URL and have no incentive to go look for it either.
    Lead me not into temptation... I can find it myself.

  5. #5
    Unregistered Leeman_s's Avatar
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    lol. im 15 in ninth grade and this stuff is EASY! i just finished algebra II

  6. #6
    Registered User JasonLikesJava's Avatar
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    Originally posted by Leeman_s
    lol. im 15 in ninth grade and this stuff is EASY! i just finished algebra II
    Me too only I'm in calculus....
    OS: Linux Mandrake 9.0
    Compiler: gcc-3.2
    Languages: C, C++, Java

    If you go flying back through time and you see somebody else flying forward into the future, it's probably best to avoid eye contact.

  7. #7
    Just because ygfperson's Avatar
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    let me restate my square root question:
    pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - .......
    pi is an irrational number
    is there a similar arrangement for irrational square roots?

  8. #8
    ¡Amo fútbol!
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    Damn, I'm in Pre-Calc and we are still in trig, using trig identities to solve trig equ's. But, we only have the courses for half a year cause my school is dumb.

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