The combination formula binomial(n,r) is now made continuous. This means that one need not go back and forth or up and down but keep moving ahead.
Here is the formula and an example with it.
That is why binomial distribution are so natural. It is continuous.
I feel ecstatic. I hope you like the expression.
Below is the Wolfram Alpha screenshots for binomial(7,2) and binomial(8,3)
Have a nice day !!
Right from my childhood I would wonder why there is no formula for a^n-b^n and a^n+b^n.
I have fulfilled this dream of mine yesterday. It took me whole Sunday to do that. 😄. My mathematical prowess is weak. But my intuitions are okay, I guess.
Here are the formulas.
They are not exactly a^n-b^n and a^n+b^n. But the values can be computed.
Have a nice day, guys !!
Here are two more binomial results
And the Wolfram Alpha results to confirm they are correct
My three consecutive number model fetch all the major constants.
I hope you like the expressions. Have a nice day !!
This result is the combination of the results posted in my last two blog posts.
This result is interesting because children often wonder there is a formula for (a+b)^n but no formula is there for a^n-b^n. Now these children have something to feel happy about.
The formula is
And the Wolfram Alpha screenshot to confirm above is true.
Have a nice day !!
The following expression is similar to the expression in my earlier blog post.
And the Wolfram Alpha screenshots to confirm the above is correct.
Have a nice day !!
Most of my mathematics was developed from intuition. I would have an intuition. And I would type them in Wolfram Alpha. And the results were obtained.
Many, many thanks to Wolfram Alpha for I was able to express my intuitions mathematically.
The following result is also one from my intuition.
Here are the Wolfram Alpha expressions to confirm that the above expression is correct. I have used a equal to 5, b equal to 7, m equal to 4 and k equal to 6.
Did you like the expression ? There are two standard binomial statements on RHS multiplied by two algebraic expressions. The numerator binomial statement starts from 1. The denominator binomial statement start from 0.
Have a nice day, guys !!
