It appears you’re looking for the summation of the expression $\sum_{k=1}^{1001} (3k - 1)$.

Solution

The expression $\sum_{k=1}^{1001} (3k - 1)$ represents the sum of the terms generated by $3k - 1$ from $k = 1$ to $k = 1001$.

Step 1: Find the General Sum Formula

The term $3k - 1$ is an arithmetic sequence where each term increases by a common difference of 3. The summation formula for an arithmetic series $\sum_{k=1}^n (ak + b)$ can be applied here, or we can calculate it term-by-term.

Since $3k - 1$ is linear, we can break the sum as follows: $\sum_{k=1}^{1001} (3k - 1) = \sum_{k=1}^{1001} 3k - \sum_{k=1}^{1001} 1$

Step