The problem is to evaluate the sum of integers from 7 to 26: \[ 7 + 8 + 9 + 10 + \ldots + 26 \] The options provided are expressed using sigma notation, which represents the sum of a sequence according to a specific rule: 1. \(\sum_{k=6}^{25} (k+1)\) 2. \(\sum_{k=7}^{26} (k+1)\) 3. \(\sum_{k=1}^{19} (k+1)\) 4. \(\sum_{k=8}^{27} (k+1)\) ### Explanation of Options: - **Option 1:** \(\sum_{k=6}^{25} (k+1)\) - Here, the variable \(k\) starts at 6 and goes to 25. Each term in the sequence is \(k+1\). - **Option 2:** \(\sum_{k=7}^{26} (k+1)\) - Here, \(k\) begins at 7 and ends at 26, adding 1 to each value of \(k\). - **Option 3:** \(\sum_{k=1}^{19} (k+1)\) - Here, the range of \(k\) is from 1 to 19, adding 1 to each value of \(k\). - **Option 4:** \(\sum_{k=8}^{27} (k+1)\) - In this option, \(k\) ranges from 8 to 27, adding 1 to each \(k\). The task is to identify which sigma notation correctly represents the sum from 7 to 26.

The problem is to evaluate the sum of integers from 7 to 26: \[ 7 + 8 + 9 + 10 + \ldots + 26 \] The options provided are expressed using sigma notation, which represents the sum of a sequence according to a specific rule: 1. \(\sum_{k=6}^{25} (k+1)\) 2. \(\sum_{k=7}^{26} (k+1)\) 3. \(\sum_{k=1}^{19} (k+1)\) 4. \(\sum_{k=8}^{27} (k+1)\) ### Explanation of Options: - Option 1: \(\sum_{k=6}^{25} (k+1)\) - Here, the variable \(k\) starts at 6 and goes to 25. Each term in the sequence is \(k+1\). - Option 2: \(\sum_{k=7}^{26} (k+1)\) - Here, \(k\) begins at 7 and ends at 26, adding 1 to each value of \(k\). - Option 3: \(\sum_{k=1}^{19} (k+1)\) - Here, the range of \(k\) is from 1 to 19, adding 1 to each value of \(k\). - Option 4: \(\sum_{k=8}^{27} (k+1)\) - In this option, \(k\) ranges from 8 to 27, adding 1 to each \(k\). The task is to identify which sigma notation correctly represents the sum from 7 to 26.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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