Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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discrete structures
![**IV. (a) Write using summation notation:**
\[ 1 + \frac{1}{3} + \frac{1}{3^2} + \ldots + \frac{1}{3^n} \]
---
**(b) Transform the summation by making the specified change of index variable \( k \) to variable \( j \) using the relationship \( j = k - 1 \):**
\[ \sum_{k=1}^{7} k(k+2)(k-3) \]
---
**(c) Write out the first four terms of the summation below. Include at least 4 terms:**
\[ \sum_{j=1}^{n} j(j-1) = \]
---
**(d) Compute the product:**
\[ \prod_{j=1}^{4} (-2)^j = \]](https://content.bartleby.com/qna-images/question/75c1327d-7664-4a3e-b58c-1991323ef32f/11d7decc-a013-46a6-872d-51a37bb409eb/7zv3kv_processed.png)
Transcribed Image Text:**IV. (a) Write using summation notation:**
\[ 1 + \frac{1}{3} + \frac{1}{3^2} + \ldots + \frac{1}{3^n} \]
---
**(b) Transform the summation by making the specified change of index variable \( k \) to variable \( j \) using the relationship \( j = k - 1 \):**
\[ \sum_{k=1}^{7} k(k+2)(k-3) \]
---
**(c) Write out the first four terms of the summation below. Include at least 4 terms:**
\[ \sum_{j=1}^{n} j(j-1) = \]
---
**(d) Compute the product:**
\[ \prod_{j=1}^{4} (-2)^j = \]
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