For posts seeking explanation or clarification of a specific step in a proof. "Please explain this proof" is off topic (too broad, missing context). Instead, the question must identify precisely which step in the proof requires explanation, 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.
Questions tagged [proof-explanation]
11824 questions
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Proof by induction help, using series
So the Question states : Show that $1^3+2^3+3^3+...+n^3=(1+2+3+...+n)^2$
This is what I have tried so far:
Let $n=1$, $1^3=1^2$, $1=1$, which is true
$1^3+2^3+3^3+...+k^3=(1+2+3+...+k)^2$ Is…
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Can you tell why the growth rate of $x^2$ is that ratio?
The hypothesis: $x \geq 4$ then $x^2 \leq 2^x$.
The proof: As $x$ grows larger than $4$, the right-side $2^x$ doubles each time $x$ increases by $1$ .
However, the left-side $x^2$ grows by the ratio $\left(\dfrac {x+1}{x}\right)^2$.
If $x \geq 4$…
parvin
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Proof by Mathematical Induction Query
How would you go about proving something like $$2^n > 5n^2$$ for all integers n>8
The part I do not understand is how to solve for $n=k+1$
Also solving for $n=k+1$ here:
$$2^n > 6n$$ for all integers n such that $n ≥ 5$
Any help is…
TheReal7
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Using induction, verify that the equation is true for every positive integer $n$.
Using induction, verify that the following equation is true for every positive integer $n$. $$r^0 + r^1 +\ldots+ r^n < \frac{1}{1−r},$$ for all $n ≥0$, and $0 < r < 1$.
I am completely stuck on how to approach this problem after the base case has…
