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Does anyone know a proof of this.

I was wondering if there was an elegant proof for the relation shown in this image.

I think I formulated the expression correctly however I failed to prove it.

Thanks.

Reply 1

TeeEm

Original post by Louisb19

I was wondering if there was an elegant proof for the relation shown in this image.

I think I formulated the expression correctly however I failed to prove it.

Thanks.

I can only think of a similar approach
(not fit at present to do any !!)

Reply 2

oShahpo

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

Reply 3

Louisb19

Original post by oShahpo

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

Thank you.

Reply 4

Zacken

Original post by Louisb19

I was wondering if there was an elegant proof for the relation shown in this image.

I think I formulated the expression correctly however I failed to prove it.

Thanks.

https://www.quora.com/What-is-a-clear-and-detailed-proof-that-the-diagonal-of-Pascals-triangle-sums-into-Fibonacci-number

Reply 5

Student403

Original post by Zacken

https://www.quora.com/What-is-a-clear-and-detailed-proof-that-the-diagonal-of-Pascals-triangle-sums-into-Fibonacci-number

Ooh that Mark Gritter guy I follow him on Quora! He went to Stanford :3

Reply 6

Zacken

Original post by Student403

Ooh that Mark Gritter guy I follow him on Quora! He went to Stanford :3

You're on Quora? I refuse to join because stackexchange is so much better. :lol:

Reply 7

Student403

Original post by Zacken

You're on Quora? I refuse to join because stackexchange is so much better. :lol:

I am but I use my irl name so I can't tell anyone :ninja:

Stack exchange is great and I go there for all my coding/programming problems but it's a lot more focused (which can be good for some and not so good for others).

I use Quora cause of the randomness of the feed which lets me learn a lot more about areas outside of my interests

Reply 8

Zacken

Original post by Student403

I am but I use my irl name so I can't tell anyone :ninja:

Ah, okay.

Stackexchange has that thing on the sidebars, I can't tell you the number of times I've ended up learning about aviation, childcare tips, cycling safety, academia, etc... :lol:

Reply 9

Student403

Original post by Zacken

Ah, okay.

Stackexchange has that thing on the sidebars, I can't tell you the number of times I've ended up learning about aviation, childcare tips, cycling safety, academia, etc... :lol:

Childcare tips/cycling safety :rofl:

I love seeing the professors and PhDs at crazy places like MIT just writing casually and explaining physics to everyone. They're amazing at breaking it down for the laymen

Reply 10

Zacken

Original post by Student403

Childcare tips/cycling safety :rofl:

I love seeing the professors and PhDs at crazy places like MIT just writing casually and explaining physics to everyone. They're amazing at breaking it down for the laymen

I know, right! I'm like "fam, you should be doing research, why are you answering my dumb question about induction" :rofl:

Reply 11

Student403

Original post by Zacken

I know, right! I'm like "fam, you should be doing research, why are you answering my dumb question about induction" :rofl:

I've thought that so many times :lol:

Reply 12

Gregorius

Original post by Zacken

I know, right! I'm like "fam, you should be doing research, why are you answering my dumb question about induction" :rofl:

I think the answer to that - and one you'll hear from many active researchers - is that reflecting on the simple basic facts of science and trying to communicate these to non-experts is extraordinarily fertile for helping think through the really hard stuff. If you can cut to what really matters, then you can cut out all the distracting junk to get to the heart of an unsolved problem.