Heavy Duty Weather Proof Multi Purpose Enclosure Amphenol Broadband 9 x 9 x 4 (Interior approx 8 x 8 x 31/2) Brand Amphenol Broadband 47 out of 5 stars 4 ratingsLet S = Consider S1= Now, this sum should be 0 or 1 based on number of natural numbers taken If infinite numbers are even, S1=0, if odd S1=1 But, Riemann zeta function gives it a value of ½ Mathematical community too agrees that the sum is ½ How?Case 2 Suppose n = 3m2 Then n 2= (3m2)2 = 9m 12m4 = 9m2 12m31 = 3(3m2 4m 1) 1 So we can write n2 = 3k 1 for k = 3m2 4m 1 Since we have proven the statement for both cases, and since Case 1 and Case 2 re ect all possible possibilities, the theorem is true 12 Proof by induction We can use induction when we want to show a New Proof That The Sum Of Natural Numbers Is 1 12 Of The Zeta Function 1+2+3+4+5 to infinity=-1/12 proof
