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## 4 questions from Sylow’s theorem: Qn 4

Prove that if |G| = 8000 then G is not simple . SOLUTION If $$|G| = 2^3 \times 10^3 = 2^6 \times 5^3 \\ consider \ , \ n_5 = (5k+1) | 2^6 \\ n_5 = 1 , 16 \\ n_2 = (2k +1) | |G| \\ \Rightarrow n_2 = 5 \ , 25 ,\ 125$$ . Let , H and K are two Sylow – 5- subgroups...

## Sum based on Probability – ISI MMA 2018 Question 24

Understand the problem The sum of Infinity series                 ( 1 + frac{2}{3} + frac{6}{3^2} + frac{10}{3^3} + frac{14}{3^4} + …….) is  Source of the problem Sample Questions(MMA) : 2018 Problem no 24 Topic Probability Difficulty Level Medium...