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SMO 2023 Open Round 1 Question 4

SMO · SMO 2023 Open Round 1

Question 4

Find the value of $\lfloor y\rfloor$, where $y=\displaystyle\sum_{k=0}^{\infty}(2k+1)(0.5)^{2k}$.

(Hint: Consider the series expansion of $(1-x)^{-2}$.)