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numerics
mediterranean
myth
variance
sand
Kringle
improbable
Boardwalk
antler
Did it make sense?
Hi 1a2b3c2212;
Look at my post, it is what he/she may have been thinking about when he/she solved the problem.
Hi 1a2b3c2212;
That statement is not true. Mathsy did not mean that.
convincing
game
meat
Hi 1a2b3c2212;
Good answer mathysperson, that is the way. In case you can't follow it, I think this is his reasoning. Normally to find the independent term (constant term) you would just set x=0, but that is not possible here, because of the x in the denominator, Start with the binomial expansion of.
The general term is:
with
So:
Pull out of the brackets all the constants and get them on the left
Set the exponents of
and equal to 0Now just plug into (A).
Hi ilovealgebra;
I was doing a similar problem a couple of days ago. I found this then:
http://qaboard.cramster.com/calculus-topic-5-164162-cpi0.aspx
this should give you everything you need.
Hi ToneMU84 and Ninja101
Hi abilash81
Welcome!
Hi Tony123 and mathsyperson;
This is a problem by Erdos, who conjectured that
would always have a solution. He did not suggest how many of them there are or how to find them. I also could not find any additional ones other than what mathysyperson has found.
Hi coffeeking;
That integral from 0 to infinity can be done analytically( the answer wil be in terms of the gamma function) . It is ≈ .232. Concentrate on the integral from - infinity to 0. That one does not converge.
Hi Stefani;
After following coffeeking's suggestion, as this is the standard way of doing it. Extend the line FN to point G. Then extend the line MN to point H
Angle FNM is 42 deg because FN bisects the angle KNM, HNG is also 42 deg because vertical angles are equal. MNG is just 180 - 42 = 138 deg
OK, I need some help here. Kris' problem is an identity, the RHS reduces to A. Does that matter?
B=1 and A>B will satisfy the criteria that
Heres how to find the limit:
Now make the substitutions
Plug them in (A). This is the new limit.
Now since (B) is of the form 0/0 we can differentiate the numerator and the denominator with respect to u. This leaves:
I think that if you prove that the limit equals a/2 with a being a positive number you will have proven that the sequence is bounded and convergent.
http://www.sosmath.com/calculus/sequence/limit/limit.html
Welcome
Hi sumpm1;
Calculators and computer algebra systems solve problems using very different methods than the human way. They have their own standards for simplification, often this will look strange. The TI 92 which is the bigger, stronger brother of the TI 89 does the exact same thing on your example. Try to use your graphing calculator to augment and check your work. Never let it replace your brain.
Here it is:
http://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means
I guess people will put 100 movies or so on it. Wow, have never seen that happen to a USB drive.
Thanks for posing it. It was really a tough problem.
Hi Tony123;
Start by forming the power series:
This will equal the terms of Tony's series if x=1. There are differences of 4 and 2 in the exponents. The expansion:
Has exponents that differ by 2.
Has exponents that differ by 4. To get differences of 4 and 2 we use a
This has the required differences of 4 then 2 in the exponents.
Now I tried to use integration, differentiation or multiplication by x on (B)
to make it look like series (A).
I couldn't. So I tried
This one doesn't have the required 4,2 difference in the exponents so it can't be right.
When I tried:
This looks good. Integrate this series and you get
(C) is series (A). So we have:
Now we need the integral.
with x=1
Hi MoyMarian;
Good way to find the minimum without Calculus, Thanks