Put your math problem and i will solve it

a^2 + b^2 + ab = 121 b^2 + c^2+ bc = 169 c^2 + a^2 + ca = 400 ab + bc + ca = ?

@ntlm said in #22:
> @Leilachess2 was I close with my estimation?
No
U were 15 years older

@marijadebe said in #8:
> Does the series \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2n-1} converge or diverge, if so, what does it converge to?
> Prove that a group of order 9 is Abelian.
> If $G$ is a non-abelian group of order 6, prove that G is isomorphic to the symmetric group $S_3$.

The series sum_{n=1}^{\infty} (-1)^{n+1} is bounded and (1/(2n-1) : n belongs to N) is a stictly decreasing
sequence of positive numbers convergent to zero. Therefore the series sum_{n=1}^{infty} (-1)^{n+1}/(2n-1)
is convergent. But I do not know how to determine its sum.

@Marcin2 said in #33:
> The series sum_{n=1}^{\infty} (-1)^{n+1} is bounded and (1/(2n-1) : n belongs to N) is a stictly decreasing
> sequence of positive numbers convergent to zero. Therefore the series sum_{n=1}^{infty} (-1)^{n+1}/(2n-1)
> is convergent. But I do not know how to determine its sum.

It is indeed convergent.
To evaluate the series, I can give you a hint. Consider the polynomial
P(x) = x-(x^3)/3+(x^5)/5-(x^7)/7+... ( the problem given is P(1) )
what happens if you differentiate the polynomial - can you find a closed form for its derivative?

1) Prove that the serie sum_{n >0} n^{-z} converges for Re(z)>1 and defines a holomorphic function in this range.
2) Prove that the said holomorphic function has a meromorphic continuation to the whole complex plane.
3) Prove that the latter only vanishes when z is a negative even integer or z has real part equal to 1/2.

@KenulL_76 said in #29:
> duude go to school again
What do you mean? @ntlm is correct in saying that 1+1 = 3. Here is the proof:

As we all know:
sqrt(1) = 1

However, I can also prove that:
sqrt(1) = sqrt [(-1)*(-1)] = sqrt(-1)*(sqrt(-1) = i*i = i^2 = -1

As a result of this, I have proven that 1 = -1

Because this is true, I can rewrite 1-1 as:
1-(-1) = 1+1

Here, we take a slight detour to solve the rather simple problem above. Consider the following:
a = b
a*b = b^2
ab-a^2 = b^2-a^2
a*(b-a) = (b+a)*(b-a)
a = b + a
a +1 = a+b+1
a+1 = 2a + 1

Now, let's assume that a = 1. That takes us back to the original problem of 1+1:
1+1 = 2(1)+1
1 +1 = 2 + 1
1+1 = 3

Therefore, it is safe to assume that 1-1 = 1+1 = 3

Proof BRIEFLY that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.

Thanks

@FC-in-the-UK said in #35:
> 1) Prove that the serie sum_{n >0} n^{-z} converges for Re(z)>1 and defines a holomorphic function in this range.
> 2) Prove that the said holomorphic function has a meromorphic continuation to the whole complex plane.
> 3) Prove that the latter only vanishes when z is a negative even integer or z has real part equal to 1/2.

And then you've got yourself 1'000'000 $. Good luck.

@anononon said in #37:
> Proof BRIEFLY that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
>
> Thanks

I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Proof BRIEFLY that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.

Thanks@marijadebe said in #38:
> And then you've got yourself 1'000'000 $. Good luck.
@marijadebe said in #39:
> I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Fermat my friend, is that you? I am still waiting for it in my dreams, miss you buddy xoxo