More complicate than the Fibonacci Sequence

This is a fibonacci-like sequence but with a twist.

[ele]

I smell a difference equation marathon coming...

[holidayeveryday]

The excitement level is not as high as the one before. Anyway amazing vid as always. Thanks!

[hellothere]

Blackpenredpen has inspired me to start my own YouTube channel! I will be uploading today! I could really use the support

[AndyGoth]

0:29 No logarithm needed to show that without the first two terms, a_n=1 for all integer n>=1. The product of 1 and 1 is 1, no matter how many times you do it. If you do apply logarithms, this turns into adding up 0 and 0, and then r will be 0.

[obnoxious]

Introducing b(n) is a bit non intuitive. Just add 1 on both sides and then you can factor. A lot more natural ;)

[universeexplorer]

I wish you can make recurrence relation marathon! Really love your videos

[sciencifier]

Why was yesterday's video deleted as soon as it was uploaded???

Love your videos 😍❤️❤️

[martind]

It seems like quite a nice way for writing it would be an = 2^Fn - 1
Where Fn is the nth Fibonacci number.

[drpkmath]

I totally agree with comment below. Might be better to have some difference equation marathon! Good one to see!

[charlesmanapat]

I'd like to have your sign one day! I'm your fan, and I also love Math. I'm a Math teacher in the Philippines btw. 😄😄😄.

[davidgillies]

Since you've recovered Binet's formula in calculating c_n, it is fairly clear that the sequence is 2^F_n - 1

[theadoenixes]

My favourite sequence 😍
Please sir can I get a heart from uh please ... I regularly watch your videos that helps me to know more and more of mathematics ... Thank you 😊

[georget]

I dont understand the reason behind the formula:
Cn = a*pos_golden_ratio + b*neg_golden_ratio

Why do we choose this formula and claim that this will calculate the fibonacci sequence?
I am not saying that this is wrong.
I am just asking which is the reason, the sequence of arguments, that will lead someone to support this formula over another.

Thank you

[farhantajwarahmed]

Loved the vidoe. Thanks, want more INTERESTING SEQUENCES!

[mrp]

nice work...well explained. Are your whiteboards are getting smaller:)

[enriquedeamoartero]

For the awesome Fibonacci's sequence (c_n), the quotient sequence c_{n+1}/c_n tends to \phi when n tends to +\infty, but do you know where does tend the sequence a_{n+1}/a_n with n going to +\infty?

[not_vinkami]

7:54 Steve: (not saying the γ joke again)
Me: Wait, that's illegal

[matthewstevens]

I solved this by adding one to both sides. You factor to get a_n + 1 = (a_n-1 +1)(a_n-2 + 1). Let b_n = a_n + 1 so b_n = b_n-1 * b_n-2. b_1=2, b_2 = 2. Then let c_n= log base 2 b_n. Therefore c_n = c_n-1 + c_n-2 with c_1=c_2=1, which is the Fibonacci sequence. Use Binet's formula and then just rearrange.

[aizazhashmi]

Please sir, I am your old fan since 2017... Please make a video on multivariable limits. To show whether the limit exists or not by using epsilon delta definition of the multivariable limits. There are lot of confusions online on this method. Please take a look at it. Lots of thanks and respect.

[alfadvestidvadtzattri]

There is another beautiful way of finding explicit formulas for recursive linear equations. You regard recursive formula like a linear operator which turns a vector of sequence members Xk, Xk+1, ... Xn into Xk+1, Xk+2, ..., Xn+1. Then the Nth power of the matrix of this operator times initial vector gives you the explicit formula for the Nth member of this sequence