ScienceMeander on Sums of Exponents ScienceMeander on Sums of a Root ScienceMeander on Undefined Sums aFrankAngle on Gratitude Grumpy Old Man on On the Boy Scout thing
My post on ∑ k ^ -n from December could perhaps use some clarifying. If C = 0 or C = 1, the sum is still simple. In December’s post, I used k as a constant and n is more … Continue reading
If k is not 1, this is simple. I’ll have to look and see how that constant denominator d does. For integer n and real k.
I like playing with math and numbers and have always liked the idea of summation formulas. This is what I played with yesterday. I started with I found it needed a constant modifier which resulted in The denominator is the … Continue reading
When we can reproduce what others have done before, that is school work. I would be interested in links to a proof of this or where it can be found elsewhere. I have not tried it with fractional exponents or … Continue reading
To keep what we have requires being able to repair and regenerate as needed. There are at least two ways to rebuild the log tables if it ever becomes necessary. The first way is kind of a reversed Sieve of … Continue reading
∞ X anything = ∞ 0 X anything = 0 But 0 X ∞ = 0 If we do anything, our efforts can be multiplied or exponentiated. If we do nothing, our efforts cannot be leveraged.
I have wondered if irrational numbers could operate on irrational numbers to produce a rational number. How to find which two rational numbers will produce a rational number? Only one irrational number is needed and any rational number … Continue reading