Q. 3 Express聽the聽sum聽3e4聽+聽3e9聽... [FREE SOLUTION]

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Chapter 13: Q. 3 (page 1003)

$Express the sum 3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} using double - summation notation .$

Short Answer

Expert verified

$3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} = {鈭�}_{j = 3}^{j = 4} {鈭�}_{k = 2}^{k = 4} {je}^{k^{2}}$

Step by step solution

Step 1. Given Information

$3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} in double - summation notation .$

Step 2. Finding common terms and converting to summation.

$3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} = (3 e^{4} + 3 e^{9} + 3 e^{16}) + (4 e^{4} + 4 e^{9} + 4 e^{16}) The common term is e^{4} + e^{9} + e^{16} and ranges from 3 to 4, which can be converted as 3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} = (3 e^{4} + 3 e^{9} + 3 e^{16}) + (4 e^{4} + 4 e^{9} + 4 e^{16}) = {鈭�}_{j = 3}^{4} {je}^{4} + {je}^{9} + {je}^{16} = {鈭�}_{j = 3}^{4} {je}^{2^{2}} + {je}^{3^{2}} + {je}^{4^{2}} The common term is e^{2^{2}} and ranges from 2 to 4, which can be converted as 3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} = {鈭�}_{j = 3}^{4} {je}^{2^{2}} + {je}^{3^{2}} + {je}^{4^{2}} = {鈭�}_{j = 3}^{j = 4} {鈭�}_{k = 2}^{k = 4} {je}^{k^{2}} Hence, 3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} = {鈭�}_{j = 3}^{j = 4} {鈭�}_{k = 2}^{k = 4} {je}^{k^{2}}$

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91影视

$Express the sum 3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} using double - summation notation .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding common terms and converting to summation.

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91影视

Expressthesum3e4+3e9+3e16+4e4+4e9+4e16usingdouble-summationnotation.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding common terms and converting to summation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

$Express the sum 3 e^{4} + 3 e^{9} + 3 e^{16} + 4 e^{4} + 4 e^{9} + 4 e^{16} using double - summation notation .$