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S=sum(i=1)^nsum(j=1)^isum(k=1)^j1...

`S=sum_(i=1)^nsum_(j=1)^isum_(k=1)^j1`

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To solve the problem \( S = \sum_{i=1}^{n} \sum_{j=1}^{i} \sum_{k=1}^{j} 1 \), we will break it down step by step. ### Step 1: Understand the innermost sum The innermost sum \( \sum_{k=1}^{j} 1 \) counts the number of terms from 1 to \( j \). Since we are summing 1 for each term, this sum equals \( j \). \[ \sum_{k=1}^{j} 1 = j \] ...
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