Recent content by willr12

Outstanding! 2^\varphi = 3.0695... And etc. Thanks! More work to come

Recently I noticed something odd about the triangular numbers. The basic definition is \displaystyle\sum_{x=1}^{n}x=T_n A short time after playing around with T_n values I discovered something very odd-another formula for triangular numbers involving the root of the sum of cubes from 1 to n...

I recently came across a problem that said 'prove that the difference of x^3+y and y^3+x is a always a multiple of 6, given that x and y are integers'. I tried it, but I'm not sure if this is a valid proof. this is with the first triangular number being 0 and Tsubn being the nth triangular number.

I understand how to calculate values of positive values ζ(s), it's pretty straightforward convergence. But when you expand s into the complex plane, like ζ(δ+bi), how do you assign a value with i as an exponent? Take for example ζ(1/2 + i) This is the sequence 1/1^(1/2+i) + 1/2^(1/2+i) +...

Each number has a digital root pattern, that's for 3. For example, 4 is 4,8,3,7,2,6,1,5,9

Digital root (adding a number's digits together repeatedly until a single digit answer is obtained) doesn't seem like a very interesting operation, but it has some weird properties. One of the first someone might notice is that dr(n) = dr(n+9) This is fairly easy to demonstrate. But after...

Y-value of the vertex in the resulting quadratic equation is -1/12. Any significance do you think? good to know thanks

It is generally accepted as a representation of Riemann zeta (-1)

Check out this graph of remainders of numbers 1-200 when divided by numbers 1-9 and let me know what you think.

Good to know. Thanks for the reply

Makes sense

Most people would stop reading when someone says that 1+2+3...=-1/12, that's counterintuitive but generally accepted...so thanks for the ignorance

okay...if you accept that the sequence 1+2+3+4...=-1/12, I think I have determined a finite value of infinity. To find the value of the sums of all natural numbers up to a number, you can use the equation ((x^2)+x)/2. An example would be 4. 4+3+2+1=10. ((4^2)+4)/2 also equals 10. following...

Me as well.

Just realized my stupidity. This equation has F1=1, F2=1, F3=2...so it starts with 1 and 1 and then goes onward instead of 0 and 1 as the first two terms. I'm working on a new equation that uses 0 and 1 as the first two. However, this equation does hold up when 1 and 1 are the first terms. When...