क्यों infinity के बारे में गलत थे Ramanujan | why Ramanujan was wrong about infintiy
Srinivas Iyengar Ramanujan was an Indian self taught genius, and was probably the only one of his kind. Scribbling, crossing, erasing, he spent most of his childhood in the alcoves of the Narasimha swamy Temple. His devotion to mathematics was such, it was often told that he loved numbers more than people. While he discovered a new theorem almost every day or perhaps even hour, he claimed Namagiri, the goddess he devoted, to appear in his dreams and let know of the theorems. Nonetheless, his genius could never be questioned. Ramanujan, like most other men of such intellect, passed away at a mere age of thirty after having discovered 2000 new theorems in his last living year, which are now stored in the three volumes, called, “Ramanujan’s lost notebook” in the libraries of Cambridge University.
While most of Ramanujan’s work hovered beyond the intellect of most people, he is the most well known among children, and adults, for his seemingly (and in real) unrealistic proof to a negative result to the sum of all natural numbers till ∞.A -1/12 also happens to pop up in string theory (not the one by Hawking but in the first theory, Bosonic string theory) which happens to explain our world to quite an extent! But could this be real? First of all, the infinite sum of all the natural number is not equal to -1/12. You can easily convince yourself of this by tapping into your calculator the partial sums
S_1 = 1
S_2 = 1+2 = 3
S_3 = 1+2+3=6
S_4 = 1+2+3+4=10
S_ n = 1+2+3+4+ ... +n
and so on. The S_ n get larger and larger the larger n gets, that is, the more natural numbers you include. In fact, you can make S_ n as large as you like by choosing So where does the -1/12 come from? The wrong result actually appeared in the work of the famous Indian mathematician Srinivasa Ramanujan in 1913 But Ramanujan knew what he was doing and had a reason for writing it down. He had been working on what is called the Euler zeta function.n large enough.
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क्यों infinity के बारे में गलत थे Ramanujan | why Ramanujan was wrong about infintiy
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