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

Explanation

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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