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JEE MAIN 2021
24-02-2021 S2
Question
Let $\mathrm{i}=\sqrt{-1}$. If $\frac{(-1+\mathrm{i} \sqrt{3})^{21}}{(1-\mathrm{i})^{24}}+\frac{(1+\mathrm{i} \sqrt{3})^{21}}{(1+\mathrm{i})^{24}}=\mathrm{k}$, and $\mathrm{n}=$ [| $\mathrm{k} \mid]$ be the greatest integral part of $|\mathrm{k}|$. Then $\sum_{j=0}^{n+5}(j+5)^2-\sum_{j=0}^{n+5}(j+5)$ is equal to $\_\_\_\_$ .
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Question Tags
JEE Main
Mathematics
Hard
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