Nettet$\sum_{i=0}^\infty i = -{1 \over 12}$ This equation in particular is said to have some importance in modern physics, but, being infotainment, there is not much detail beyond that. As an IT Major, I am intrigued by the implications of this, and also the mathematical backgrounds, especially since this equality is also used in the expansion of the domain … Nettet25. mar. 2024 · The series is clearly divergent, besides which adding up a bunch of positive integers is not ever going to result in -1/12. But the Riemann zeta function can be analytically continued over to s = -1 in the complex plane. Zeta cannot be expressed in terms of the series above in that region, but entirely different methods show that zeta( …
Using Euler
Nettet18. feb. 2024 · 3.2: Direct Proofs. In Section 3.1, we studied the concepts of even integers and odd integers. The definition of an even integer was a formalization of our concept of an even integer as being one this is “divisible by 2,” or a “multiple of 2.”. NettetCounting Integers in a Range. How many integers are there from 1 to 10? That's easy, it's 10. How do you get the answer 10? First of all, "1 to 10" represents the closed interval [1, 10] [1,10]; to get 10 we simply subtract the left endpoint from the right endpoint and then add 1, i.e. 10-1+1=10 10−1+ 1 = 10. power company with bad credit
Why is the sum over all positive integers equal to -1/12?
NettetFactor Pairs of 12 are combinations of two factors that when multiplied together equal 12. Here are all the Positive Factor Pairs of 12. 1 × 12 = 12. 2 × 6 = 12. 3 × 4 = 12. 4 × 3 = 12. 6 × 2 = 12. 12 × 1 = 12. Like we said above, Factors of 12 include negative numbers. Nettet1. jul. 2024 · We see that amongst any group of 12 integers, there is always going to be two numbers who sum is a multiple of 10, and who have the same tens digit (for … power company that services my area