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Sense does any make 2mm multiply reason Q: how does “1+2+3+4+5+… = -1/12” make any sense? Mathematical induction: prove that 1^3 + 2^3 +3^3 n^3 = n^2 {(n+1
Q: How does “1+2+3+4+5+… = -1/12” make any sense? | Ask a Mathematician
Number 10 icon #388295 Number shadow webstockreview Induction prove mathematical
%5Czeta(s)%5C%5C[2mm]++%3D%26%5Cleft(1-2^{1-s}%5Cright)%5Csum_{n%3D1}^%5Cinfty%5Cfrac{1}{n^s}%5C%5C[2mm]++%3D%26%5Csum_{n%3D1}^%5Cinfty%5Cfrac{1}{n^s}-2^{1-s}%5Csum_{n%3D1}^%5Cinfty%5Cfrac{1}{n^s}%5C%5C[2mm]++%3D%26%5Csum_{n%3D1}^%5Cinfty%5Cfrac{1}{n^s}-2%5Csum_{n%3D1}^%5Cinfty%5Cfrac{1}{(2n)^s}%5C%5C[2mm]++%3D%26%5Cleft(%5Cfrac{1}{1^s}%2B%5Cfrac{1}{2^s}%2B%5Cfrac{1}{3^s}%2B%5Cfrac{1}{4^s}%2B%5Cldots%5Cright)-2%5Cleft(%5Cfrac{1}{2^s}%2B%5Cfrac{1}{4^s}%2B%5Cfrac{1}{6^s}%2B%5Cfrac{1}{8^s}%2B%5Cldots%5Cright)%5C%5C[2mm]++%3D%26%5Cfrac{1}{1^s}-%5Cfrac{1}{2^s}%2B%5Cfrac{1}{3^s}-%5Cfrac{1}{4^s}%2B%5Cldots%5C%5C[2mm]++%3D%26%5Csum_{n%3D1}^%5Cinfty%5Cfrac{(-1)^{n-1}}{n^s}%5C%5C[2mm]++%3D%26%5Csum_{n%3D0}^%5Cinfty%5Cfrac{(-1)^{n}}{(n%2B1)^s}++%5Cend{array}&bg=ffffff&fg=000&s=0)