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#3350. Which is the prime number divisible by
?
I have been reading posts back and forth about this. This sum,
which is even, does not divide any prime number.
The question could have been "Which prime number divides this sum?"
2 would be an answer.
But, if the question meant was to determine the largest prime
number that divides (into) this sum, then the question stated
should be along the lines of:
"What is the largest prime that divides
You are welcome and nice to see you are not rusty.
New problem:
Prove:
When n>0
This section would contain any question under the sun, sometimes mathematics too!
1. What are Deimos and Phobos?
The answer given is not the only one. Unless the question is narrowed down,
think
A new problem:
What is the area of the largest triangle that can fit inside of a square with sides s?
What type of triangle is it?
This is not a proof. You have to account for the fact
that certain triangles have heights greater than s units.
Then show that, if true, their bases would have to be
too small so that
The answer to the exercise in post #1109 still has not been posted.
Hi folks,
Gotta solve this one as well. Any help appreciated.
For which non-negative integers is
n² ≤ n! ?Answer to be proven with math induction.
regards
John J
User TheDude, there is a factorial sign in that exercise.
Another way:
Assume S is a finite sum.
Group it as:
S = 1 + [(1/2 + 1/3 + 1/4) + (1/5 + 1/6 + 1/7) + (1/8 + 1/9 + 1/10) + ...] > **
1 + [3(1/3) + 3(1/6) + 3(1/9) + ...] =
1 + [1 + 1/2 + 1/3 + ...] =
1 + S
But this has S > 1 + S.
This is impossible if S is to have a finite value.
So this is a contradiction, and therefore S must
not have a finite sum.
That is, S is divergent.
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Can anyone help me, how to derive the formula of the volume of the cone 1/3*pi*r^2*h ?
The volume of a right circular cone with radius r and height h, equals the
area of the right triangle (let the base = r and the height = h), which is
being revolved along the line containing the line segment h, multiplied by the
circumference using the r/3 part of the centroid* as the radius of revolution.
The centroid of a triangle is where all of its medians intersect.
The centroid is the geometric center of the triangle.**
Then the formula for the volume is
the area of the triangle, multiplied by the circumference at the
geometric center (centroid), and using r/3 as the radius of revolution.
This is:
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* Suppose a right triangle is situated on the xy-plane with the
radius extending from (0, 0) to (r, 0) and the height extending
from (0, 0) to (0, h).
The x-coordinate of this centroid is r/3. (This can be worked out using
coordinate geometry.)
** Source:
http://en.wikipedia.org/wiki/Centroid
A quadrilateral PQRS has angular bisectors of angle S
and angle P which meet inside the quadrilateral at a point O.Does the measure of angle Q + the measure of angle P =
twice the measure of angle SOP?No other clues are visible
For instance, it *does* work for a quadrilateral when it is a square.
However, I am looking for a counterexample with the following:
I will start with:
Again, assume S is a finite sum.
S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...
S = 1 + (1/2 + 1/3) + (1/4 + 1/5) + (1/6 + 1/7) + (1/8 + 1/9) + ...
S = 1 + (5/6) + (9/20) + (13/42) + (17/72) + ...
Hi Darby;
I am sorry but I have been unable to find anything for those
that does not use something more complicated then what
you have been using.
10:38
1 = [0(3 + 8)]!
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10:47
1 = [0(4 + 7)]!
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10:57
1 = [0(5 + 7)]!
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10:58
1 = [0(5 + 8)]!
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10:59
1 = [0(5 + 9)]!
__________________
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1 = (0 X 2 X 7)!
1 = (0/2 X 7)!
1 = [0 X (2 + 7)]!
1 = [0 X (2 - 7)]!
1 = [0 X 2^7]!
1 = [0/(2^7)]!
1 = (0^27)!
1 = [0^ (2 X 7)]!
1 = [0^(2^7)]!
1 = [(0^2)^7]!
1 = [0^2 X 7]!
1 = [0^(2/7)]!
1 = [(0/2)/7]!
1 = [(0 X 2)/7]!
1 = (0/2/7)!
1 = (0/2 X 7)!
1 = (0/27)!
1 = [0/(2 X 7)]!
1 = [(0 X 2)^7]!
1 = [(0/2)^7]!
1 = [0/(2^7)]!
1 = [0/(2 + 7)]!
.
It need not be a person. Certain animals have a concept of numbers and counting.
And numbers, (counting numbers, for instance) have their own existence independent
of human thought. Before there were humans to think about numbers,
there were always places where there was one thing, two things, etc.That's very interesting. If it's true, I don't think it changes my argument;
But which animals did you have in mind?
just substitute 'some animals including humans' for 'person'.
Certain chimpanzees
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but three doesnt exist except in the mind of a mathematically inclined person.
It need not be a person. Certain animals have a concept of numbers and counting.
And numbers, (counting numbers, for instance) have their own existence independent
of human thought. Before there were humans to think about numbers,
there were always places where there was one thing, two things, etc.
So, in certain circumstances, its ok to say 3 + 4 = 7.
But, notice this rule doesnt always work. If I walk 3 miles and then walk 4 miles,
I'm not necessarily 7 miles away from where I started.
This is not a correct example of "a rule that doesn't always work,"
as you put it. You're comparing apples and oranges. Those movements equal
a total of 7 miles walked. The rule works. Mixing in where someone ended
up relative to the starting point is changing the subject.
So, for instance, when we make the rule for powers:
we find it works ok with all the other stuff we know about powers.
Then when someone poses the question I wonder if we can find a sensible meaning for:
the answer is, yes, we can. It makes good sense to let it have the value 1 because this
is consistent with the rule of powers:
You have made a blanket statement. It is not so where x = 0.
Under that method,
So 0^0 could equal 1,
I want everyone to see this, so I did not hide it:
Prove that the Harmonic series is divergent.
Let S = the Harmonic series.
Assume S has a finite value.
S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ...
S = (1 + 1/2) + (1/3 + 1/4) + (1/5 + 1/6) + ...
> (2/2) + (2/4) + (2/6) + ...
= 1 + 1/2 + 1/3 + ...
= S
But this states that S > S, which is impossible,
because S is assumed to be finite.
So, this is a contradiction, and the Harmonic series
is divergent.
Without using either of the two specific methods shown at this
Wikipedia site (in the top first few pages), use an alternate
method to prove the divergence of the Harmonic series:
http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
How long ago was
thor around, according to myth?Is it really only 300 years ago?
LQ,
"Thor" is a proper noun, so it is capitalized.
This game assumes that the car is the prize and the goat
is not. If I were a young child playing it, I wouldn't switch
if I already had the goat in view, because I like goats,
and I would have no use for a car.
look at it this way: 0,5 is just another way of representing 1/2,and by the same logic 0,3333... recurring is just another way of representing as 1/3.
Also, don't forget to include that
IMMORTALX,
post all of your work/attempts at the problems
first so that you may be helped where you are
stuck. Your input is needed, and none of the
answers on any of your threads should just be
delivered to you. We're to be coaches, and
you're to be the athlete who does the work/practice
so you can be guided in a better direction.
IMMORTALX,
post your work/attempts first so that you may be
helped with where you are stuck.
IMMORTALX,
post your work/attempts first so you may be helped
with where you are stuck.
IMMORTALX,
you have to post your work thus far (your attempts),
so that you can be helped. Show us where you are
stuck by showing your work . . . first.