Chapter 13: Q. 6 (page 1003)

$How many summands are in {鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k} ?$

Short Answer

Expert verified

$Total number of summands in {鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k} are (k_{0} - n + 1) 脳 (j_{0} - m + 1)$

Step by step solution

Step 1. Given Information

${鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k}$

Step 2. Finding summands

${鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k} = {鈭�}_{j = j_{0}}^{m} ({鈭�}_{k = k_{0}}^{n} j^{k}) The summation {鈭�}_{k = 5}^{20} \frac{j^{2}}{e^{jk}} can be expanded by replacing k with k_{0} and rewriting each term when k ends at n . The number of terms in above summation are k_{0} - n + 1 . Similarly when expanded {鈭�}_{j = j_{0}}^{m} ({鈭�}_{k = k_{0}}^{n} j^{k}) by replacing j from j_{0} to m, the number of {鈭�}_{k = k_{0}}^{n} j^{k} terms obtained are j_{0} - m + 1 Hence total number of summands are = (k_{0} - n + 1) 脳 (j_{0} - m + 1) Total number of summands in {鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k} are (k_{0} - n + 1) 脳 (j_{0} - m + 1)$

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$How many summands are in {鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k} ?$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding summands

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Howmanysummandsarein鈭�j=j0m鈭�k=k0njk?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding summands

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

$How many summands are in {鈭�}_{j = j_{0}}^{m} {鈭�}_{k = k_{0}}^{n} j^{k} ?$