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SMO 2020 Open Round 1 Question 3

SMO · SMO 2020 Open Round 1

Question 3

Let $S_n=\dfrac1{1\times3}+\dfrac1{3\times5}+\dfrac1{5\times7}+\cdots+\dfrac1{(2n-1)\times(2n+1)}$. Find the value of $n$ such that $S_n$ takes the value of $0.48$.