About 4 years back a thought came in my mind. 1 to 2 is hundred percent rise. But 99 to 100 is just about one percent rise. Is there any "constant" for this I wondered.
I will explain it. Only today it became clearer.
Consider 1/1, 1/2, 1/3 and so on. It decreases considerably.
Now consider 1/2,2/3,3/4 and so on. It increases but not considerably.
If we take to the power of 1/2,2/3,3/4 and so on then the increase may be considerable.
So the "constant" I wrote in first paragraph is 1/n +log(n)-log(n+1) summed up for n from 1 to infinity. Isn't it?
Well that is what is Euler-Mascheroni constant. Gamma. 0.577. . . . .
How is this for beauty ? My master Euler it was. Amazingly beautiful !!
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