sequence divergence proof

[shelly89]

Can someone please explain this proof to me, I dont understand how \(\displaystyle N = 4M^{2} \)

 

[stapel]

I dont understand how \(\displaystyle N = 4M^{2} \)

The "how" is because they "let" ("decided", "created the expression and made it so") the one be equal to the other.

 

[shelly89]

The "how" is because they "let" ("decided", "created the expression and made it so") the one be equal to the other.

I see, but why specifcally choose 1/4?

 

[Romsek]

I see, but why specifcally choose 1/4?

what they did (while you weren't looking) was to work the problem backwards starting from the last statement a_n > M.

That ended up requiring that \(\displaystyle N=\left\lfloor 4 M^2\right\rfloor\) and so by choosing N to be this value they worked the problem forwards (while you were looking) to show a_n > M.

 

[DrPhil]

I dont understand how [FONT=MathJax_Math]N[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math]M[/FONT][FONT=MathJax_Main]2[/FONT]

The "how" is because they "let" ("decided", "created the expression and made it so") the one be equal to the other.

A more interesting question would be "Why," instead of "How." If you look through the proof, you will suddenly see a step where the square root of N must be greater than 2M. So make that an initial statement!

It is sort of like Jeopardy, where you have to find a question for a given answer.

 

[shelly89]

I understood it now, thank you.