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Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is my proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

This tag should be used when you have a proposed solution to a problem and have specific concerns or doubts about the validity of that solution. A question with this tag should include an explanation for why the argument presented is not convincing enough. Further discussion on using this tag can be found in the Mathematics Meta questions (1) and (2).

Answers to questions tagged look first and foremost to check that the solution is right, and to comment upon the approach taken by the author of the question. If the proposed solution is wrong, a good answer would explain where or how mistakes were made, and possibly give or sketch a correct solution instead.

If the proposed solution is correct, an answer would ideally provide further evidence to back the answerer's opinion. These could include a clearer rewriting of the given argument, alternative arguments, generalizations of the proven result, or careful consideration of unexpected subtle points. Users looking to write answers can find further discussion in this Mathematics Meta post.

21426 questions
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Proof Verification: Prove $15^n+6^{2n+1}$ is divisible by 7 for all $n\in \mathbb{N}$

Let $P\left(n\right)$ be the statement that $15^n+6^{2n+1}=7m$ for some $m\in \mathbb{N}$ Prove the base case of $n=0$: $P\left(n\right)=15^0+6^1=7$ which is divisble by 7. Therefore, is true for $n=0$. Assume $P(n)$ holds truth for some…
charl2.718
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Show that $(x_n)=\dfrac{n}{n^2+1}$ converges to zero.

Show that $(x_n)=(\frac{n}{n^2+1})$ converges to zero. Here's the definition of convergence: $$\forall \epsilon > 0, \exists N \in N s.t (n\geq N) \implies |{a_n-L}|<\epsilon$$ By solving I get $$\frac{1}{n}<\epsilon$$ Why should I choose the N to…
Mengen Liu
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Is this proof done wrongly?

I have tried for hours at this problem, but feel as if there is no way to prove it. Isn't this just false? n > 0. $$\sum_{k=0}^n \frac{1}{2^k} = 2 = \frac{1}{5^n}$$ I keep getting false because 2(left hand sided answer) is NOT equal to 3/2 (which is…
Ariani P.
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Find distance between two points. Time and Speed

An urgent message had to be delivered from the house Of the Peshwas in Pune to Shivaji who was camping in Bangalore. A horse rider travels on horse back from Pune to Bangalore at a constant speed. If the horse increased its speed by $6km/h$, it…
Joypal
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Compact set, contained in compact set, contained in an open set

Statement : In $\mathbb{R}^{n}$, if $U$ is open and $C \subset U$ is compact, show that there is a compact set $D$ such that $C \subset$ int$(D)$ and $D \subset U$. I want to see if the proof is correct, and more over if it can be shortened. Also,…
Avijit Dikey
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Is this expression greater than 1?

I'm studying physics (sorry) and can't for the life of me express the following as greater than one. All $T$s are values for temperature, and thus greater than 0. $\frac{T_0^2}{T_HT_C}$ (should be) > 1 where $T_0=\frac{1}{2}(T_H+T_C)$. Very…
N Godrich
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Verifying the method when $x^2+y^2=1$.

Before I show my method, I'll post an example question. (Also, this one is the start of my wonder.) $x^2+y^2=1, z^2+w^2=1$. Then, find the minimum and maximum of $xw+yz$. Of course, It can be easily solved with the Brahmagupta-Fibonacci…
RDK
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G. Bartle R. Sherbet "Introduction to real analysis" problem 7 sections 2.3.

I proved one statement. Can somebody check, did I make it correct and mathematically precise? If $S \subseteq \mathbb R$ contains one of its upper bound, show that this upper bound is the supremum of $S$. $\underline{\textbf{Proof}}$: So let $S$ be…
mathguruu
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Prove decay function concaved-up

Below decay function were used for solving TVM, for interest rate. $\displaystyle f_n(x) = \frac{n\;x}{(1+x)^n-1}\qquad$, where $n>1,\;x>-1$ I wanted to show decay function is concaved-up. In other words, I wanted to show $f_n^{''}(x) > 0$ This is…
albert chan
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Why is the reciprocal of i equal to i and also -i?

I know that $\dfrac{1}{i}=-i$. However, $\sqrt{\dfrac{-1}{1}}=\sqrt{\dfrac{1}{-1}}$, so $i=\dfrac{1}{i}$. What am I missing here?
Thuong Vo
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Why might this answer to a differential question be false? Is there a more rigorous proof or counterexample?

I'm trepidatious to accept an answer here because there's a couple points the author hasn't cleared up Why doesn't this differential technique work? $y''/y$ certainly exists if the solution exists wherever $y \neq 0$, and it is integrable. Secondly,…
StackQuest
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Prove: $f(A \cup B)=f(A) \cup f(B)$

I would like to get some feedback if this proof is rigorous and correctly written. And if not how should it be written. Where did I go wrong etc. Def 1: $x \in A \cup B: \Leftrightarrow \forall x: x \in A$ or $x \in B$ Def 2: $f(A)=\{Y \in Y \mid…
ALEXANDER
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$f(A) \subseteq f(B)$ whenever $A \subseteq B$

I am looking for feedback if this would constitute a proof, I feel like it is more a explanation than a rigorous proof: Please provide feedback where it is wrong/inadequate and how it should be done to become rigorous. Prove: $f(A) \subseteq f(B)$…
ALEXANDER
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Proof of ex. from 'The nuts and bolts of Proofs'

In a book (The nuts and bolts of Proofs) there is the exercise: If $n$ is a three-digit number, whose unit digit is at most 4, whose hundred digit is between 1 and 5, and whose tens digit is the sum of the other two digits, then n is divisible by…
Dimitris
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Prove that if that if $p > \sqrt{n} + \sqrt{n+1}$ where $n \in\Bbb N$*; then $p² \ge 4n + 2$

Here's what I tried: $$p > \sqrt{n} + \sqrt{n+1}$$ $$p² > (\sqrt{n} + \sqrt{n+1})²$$ $$p² > 2n + 1 + 2\sqrt{n(n+1)}$$ So we need to prove that $$2n + 1 + 2\sqrt{n(n+1)} > 4n + 2$$ $$2n + 1 - 2\sqrt{n(n+1)} < 0$$ $$n + \frac{1}{2} <…
Amin Guermazi
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