Chapter 13: Q. 5 (page 1003)

$How many summands are in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} ?$

Short Answer

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$Total number of summands in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} are 176$

Step by step solution

Step 1. Given Information

$\sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}}$

Step 2. Finding number of summands

$\sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} = \sum_{j = 3}^{13} (\sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}}) The summation \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} can be expanded by replacing k with 5 and rewriting each term when k ends at 20 . \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} = \frac{j^{2}}{e^{j 5}} + \frac{j^{2}}{e^{j 6}} + \frac{j^{2}}{e^{j 7}} + . . . + \frac{j^{2}}{e^{j 20}} The number of terms in above summation are 20 - 5 + 1 = 16 . \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} = \sum_{j = 3}^{13} (\sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}}) = \sum_{j = 3}^{13} (\frac{j^{2}}{e^{j 5}} + \frac{j^{2}}{e^{j 6}} + \frac{j^{2}}{e^{j 7}} + . . . + \frac{j^{2}}{e^{j 20}}) Similarly when expanded \sum_{j = 3}^{13} (\frac{j^{2}}{e^{j 5}} + \frac{j^{2}}{e^{j 6}} + \frac{j^{2}}{e^{j 7}} + . . . + \frac{j^{2}}{e^{j 20}}) by replacing j from 3 to 13, the number of \frac{j^{2}}{e^{j 5}} + \frac{j^{2}}{e^{j 6}} + \frac{j^{2}}{e^{j 7}} + . . . + \frac{j^{2}}{e^{j 20}} terms obtained are 13 - 3 + 1 = 11 Hence total number of summands are = 16 \times 11 = 176 Total number of summands in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} are 176$

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$How many summands are in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} ?$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding number of summands

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Howmanysummandsarein∑j=313∑k=520j2ejk?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding number of summands

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Most popular questions from this chapter

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$How many summands are in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} ?$