Proofs 🥲 (1 Viewer)

Hello_World2 · Nov 14, 2022

I don't have a clue of where to start this question? Can someone pls help ? Thanks !

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cossine · Nov 14, 2022

Hello_World2 said:
I don't have a clue of where to start this question? Can someone pls help ? Thanks !
View attachment 37024

I think polynomials was part old syllabus. But the theorem you are looking for is rational root theorem. This should provide the answer a/b.

https://en.wikipedia.org/wiki/Rational_root_theorem

Hello_World2 · Nov 19, 2022

Bruh, for questions 4 and 5 I tried doing it, and then it got too complicated to solve. What am I doing wrong ??

Pls help thanks

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Hello_World2 · Nov 19, 2022

yess i got it thanks !

Drongoski · Nov 19, 2022

For Q5:

$\text {Assume true for }n=k \geq 6 \implies \frac{1}{k!} < \frac {1}{e^k}\\ \\ \therefore \frac {1}{(k+1)!} = \frac {1}{k!} \times \frac {1}{k+1} < \frac {1}{e^k} \times \frac {1}{k+1} < \frac {1}{e^k} + \frac {1}{e} = \frac {1}{e^{k+1}} \\ \\ \text {since, for k greater than 5: } \frac {1}{k+1} <\frac {1}{e}$

So there you are.

Q4 requires quite a bit of LaTeX; so I'll give it a miss at the moment.

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