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Find the value of the following sums. For b., round to 2 decimal places. Please show your work if you want credit. You can't just use Excel or some other such method but must use the formulae. a. ΣΞo 4· (-3)* b. Σ4515(1.5)*

Find the value of the following sums. For b., round to 2 decimal places. Please show your work if you want credit. You can't just use Excel or some other such method but must use the formulae. a. ΣΞo 4· (-3)* b. Σ4515(1.5)*

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Summation Problems **Instructions:** Find the value of the following sums. For part **b**, round your answer to 2 decimal places. Please show all your work for full credit. You cannot use Excel or any other computational tools; you must use the formulae. #### Problems: **a.** \(\sum_{k=0}^{12} 4 \cdot (-3)^k\) **b.** \(\sum_{k=15}^{45} (1.5)^k\) In these problems, the summation notation \(\sum\) is used, indicating that you need to sum a sequence of terms. Each term in the sequence is determined by substituting integer values of \(k\) into the given formula, starting from the lower index value and ending at the upper index value. In problem **a**, you first calculate each term by substituting values of \(k\) from 0 to 12 into the expression \(4 \cdot (-3)^k\), and then sum those terms. In problem **b**, you calculate each term by substituting values of \(k\) from 15 to 45 into the expression \((1.5)^k\), and sum those terms. **Note**: Be sure to show all calculations step-by-step for partial credit.
Transcribed Image Text:### Summation Problems **Instructions:** Find the value of the following sums. For part **b**, round your answer to 2 decimal places. Please show all your work for full credit. You cannot use Excel or any other computational tools; you must use the formulae. #### Problems: **a.** \(\sum_{k=0}^{12} 4 \cdot (-3)^k\) **b.** \(\sum_{k=15}^{45} (1.5)^k\) In these problems, the summation notation \(\sum\) is used, indicating that you need to sum a sequence of terms. Each term in the sequence is determined by substituting integer values of \(k\) into the given formula, starting from the lower index value and ending at the upper index value. In problem **a**, you first calculate each term by substituting values of \(k\) from 0 to 12 into the expression \(4 \cdot (-3)^k\), and then sum those terms. In problem **b**, you calculate each term by substituting values of \(k\) from 15 to 45 into the expression \((1.5)^k\), and sum those terms. **Note**: Be sure to show all calculations step-by-step for partial credit.
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