Linkey Posted June 23 Share Posted June 23 I have watched a video about the p-adic numbers: Then, there is the Ramanujan's summation which is used in quantum mechanics (Casimir effect): 1+2+3+4+5+6...=-1/12 https://en.wikiversity.org/wiki/Quantum_mechanics/Casimir_effect_in_one_dimension This forum does not support Latex maths? Then, we have one more such summation: 1+x+x*x+x*x*x+x*x*x*x+x*x*x*x*x...=-1/(1-x) This is simple for x<1 and for x>1 we get: 1+2+4+8+16+32+64...=-1 1+10+100+1000+10000...=-1/9 1+20+400+8000+160000...=-1/19 Can we obtain all these sums with the p-adic numbers? Link to comment Share on other sites More sharing options...
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