Question
$N$, the set of natural numbers, is partitioned into subsets $S_{1}=\{1\}, S_{2}=\{2,3\}, S_{3}=\{4,5,6\}, S_{4}=\{7,8,9$ $10\}$. Find the sum of the elements in the subset $S_{50}$.
Step 1
For example, the last element of $S_{1}$ is 1, the last element of $S_{2}$ is 3, the last element of $S_{3}$ is 6, and so on. This pattern can be represented by the formula $n(n+1)/2$. Show more…
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If $\mathrm{A}_{1} \subset \mathrm{A}_{2} \subset \mathrm{A}_{3} \subset \ldots \subset \mathrm{A}_{50}$ and $\mathrm{n}\left(\mathrm{A}_{\mathrm{x}}\right)=\mathrm{x}-1$, then find $\mathrm{n}\left[\bigcap_{\mathrm{x}=11}^{50} \mathrm{~A}_{\mathrm{x}}\right]$. (1) 49 (2) 50 (3) 11 (4) 10
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