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# The Proof is Trivial! Watch

1. Problem 506

This is a very nice one indeed, evaluate:

2. (Original post by Zacken)
It's called Latex, and here's how you use it on TSR.
I thank you, good sir
3. (Original post by Alexion)
I thank you, good sir
You're welcome, have a stab at my previous integral, you'll find it a valiant challenge.
4. (Original post by Zacken)
You're welcome, have a stab at my previous integral, you'll find it a valiant challenge.
Haha, I'll pass it's late, and I'm not the best at these sorta challenges anyway
5. (Original post by Alexion)
Haha, I'll pass it's late, and I'm not the best at these sorta challenges anyway
Fair enough.

Anyways, what's your story, A-Levels, degree maths, prospective mathmo?
6. (Original post by Zacken)
Fair enough.

Anyways, what's your story, A-Levels, degree maths, prospective mathmo?
A-level Further Mathematician prospective Electronic Engineer actually...
Doesn't stop me from being that nerd who aced C3 though
7. (Original post by Alexion)
A-level Further Mathematician prospective Electronic Engineer actually...
Doesn't stop me from being that nerd who aced C3 though
Filthy engineer.

Kidding, kidding. Y12 or 13?
8. (Original post by Zacken)
Filthy engineer.

Kidding, kidding. Y12 or 13?
Y13... only 31/2 people in our FM class, it's great

All the easier to brag about my higher test and exam scores
9. (Original post by Alexion)
Y13... only 31/2 people in our FM class, it's great
1/2? Do I want to ask? xD
10. (Original post by Zacken)
1/2? Do I want to ask? xD
Yeah, we sliced him up and threw the other half out the window

Nah, it's just that he dropped the subject at A2, so he's only in half of our lessons now (hence the .5)
11. (Original post by Alexion)
Yeah, we sliced him up and threw the other half out the window

Nah, it's just that he dropped the subject at A2, so he's only in half of our lessons now (hence the .5)
What's the M/F ratio in that class?
12. (Original post by Zacken)
What't the M/F ratio in that class?
#DIV/0!

All guys
13. (Original post by Zacken)
Problem 506

This is a very nice one indeed, evaluate:

Set then

So therefore
14. (Original post by Kummer)
Set then

So therefore
That's certainly one way to do it, bravo!
15. Problem 507

Does the series

Converge as ? If so, to what value.
16. Problem 508

is an N x N matrix with N distinct eigenvalues all in the range . Prove that:

Converges. {NB: I denotes the N x N identity matrix}
17. Problem 509

Let be the sides of a triangle. Prove that
18. (Original post by 16Characters....)
Problem 507
Solution 507

You like your convergence questions, don't you?

By the ratio test, we have

.

So our series converges. To determine what is converges to is slightly easier to see if we define so that our series becomes

This looks suspiciously like a certain well-known McLaurin series, so lo and behold:

.

This was fun!
19. (Original post by Zacken)
Solution 507

You like your convergence questions, don't you?
This was fun!
Haha maybe... :-)
20. (Original post by 16Characters....)
Haha maybe... :-)

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