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Nov
24
comment How to find the sum of this : $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+ \sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+…$
@user158108: $$n^2 \cdot (n+1)^2 + n^2 + (n+1)^2=n^4+2 n^3+3 n^2+2 n+1$$ But polynomial equations of type $$x^4+ax^3+bx^2+ax+1=0$$ can be transformed to $$(x^4+1)+ax(x^2+1)+bx=0$$ and further to $$x^2((x+\frac{1}{x})^2-2)+a(x+\frac{1}{x})+c)=0$$ Now the substitution $$y=x+\frac{1}{x}$$ can be used.
Nov
24
comment An interesting table of Prime Generating polynomials similar to $n^2+n+41$?
To me it seems that these are at least 5 questions.
Nov
24
comment Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$
and you start with which $n$? For $n=1$ you get $0=f(1)=f(2)=?$
Nov
24
comment Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$
Why do you use two different notations for the numbers? Either $f(n)$ of $F(n)$. Then numbers are $0,1,1,2,3,5,\ldots$. So if $f(5)=5$ then $f(1)=1, f(3)=2$.
Nov
21
comment $P(x+2)=2x^3-4x^2+2x+3$. Find the remainder of $\dfrac{P(x)}{(x-3)}$
What does $P(u)=2(x-2)^3-4(x-2)^2+2(x-2)+3$ mean? Do you want the remainder of $P(x)/x-3=\frac{P(x)}{x}-3$ or of $P(x)/(x-3)=\frac{P(x)}{x-3}$
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
How is a function $F(x)=\int_0^xf(t)dt$ connected with the antiderivates? It is an antiderivate of $f$ if $f$ is continous, so $F'(x)=(\int_0^xf(t)dt)'=f(x)$. To see this one has to proof that $\lim_{h \to 0} \frac{F(x+h)-F(x)}{h}=\lim_{h \to 0} \frac{\int_0^{x+h}f(t)dt-\int_0^xf(t)dt}{h}=\lim_{h \to 0} \frac{\int_x^{x+h}f(t)dt}{h}$ is equal to $f(x)$
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
For example select $a=0$ and $f(t)=t^2$ and therefore $F(x)=\int_0^x t^2 dt$. So for $x=3$ the function value $F(3)$ is the definite integral $\int_0^3 t^2 dt$, which is $9$, for $x=4$ the function value $F(4)$ is the definite integral $\int_0^4 t^2 dt$, which is $64/3$
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
you are right, thank you
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
Does your book (which book?) really say it is a family of equations? I think it should say it is a family of functions.
Nov
17
comment Union of Two Rectangles is the Disjoint Union of at most $6$ Rectangles
Can you show an example for $X = \mathbb R \times \mathbb R$ where 6 rectangles are needed?
Nov
17
comment Does $a\ln(x^2 +y^ 2 )+b$ satisfy Laplace’s equation?
your calculations are right and $F_{yy} = -F_{xx}$
Nov
16
comment Show that no linear polynomial divides $x^k + x^{k-1} + \cdots + 1$ with $k\ge 2$ even
$x^3+x^2+x+1=(x+1)(x^2+1)$
Oct
26
comment can any identity involving integers be proved by mathematical induction
Can you add the principle of mathematical induction, nth principle of mathemactical induction and the extended principle of mathematicla induction to your post?
Oct
6
comment Logarithms in Calculators?
Maybe you calculatore uses reverse polish notation. So add a link to a manual of your calculator if possible.
Oct
6
comment Logarithms in Calculators?
What calculator do you use?
Sep
30
comment Is the sum of all natural numbers $-\frac{1}{12}$?
So how does your new definition of convergence looks like? What are the implications of this change? When is this change of the definition useful? I can't see this this.
Sep
30
comment Problems in elementary number theory and methods from physics
-1 It seems to me that this answer is completely off topic. Neither is 2+2 the such a number theoretic topic in the sense of the OP nor does it help to think of a calculater if one wants to make an addition ot two numbers.
Sep
30
comment Problems in elementary number theory and methods from physics
I think it is hard to find application of number theory in physics. Of course its even harder to find applications of number theory in physic that can be solved by "physical" reasoning
Sep
27
comment The Largest Prime Less Than the Square of a Prime
It is listed as A054270. But I can't see that it has been "studied"? I cannot find any reference to a paper there.
Sep
25
comment Arrangement of 5 letter words
Why $26 \cdot 25 \cdot 24 \cdot 25 \cdot 26$?