(a) Place the following in increasing order (from smallest to largest). You do not need to give expla- nations. A = Σ B = k=100 Σ k=1 C = 3 1 2k + 3k 1 2k + 3k D = Ε Ξ k=1 1 แผง Σ k=1000 1 3k
(a) Place the following in increasing order (from smallest to largest). You do not need to give expla- nations. A = Σ B = k=100 Σ k=1 C = 3 1 2k + 3k 1 2k + 3k D = Ε Ξ k=1 1 แผง Σ k=1000 1 3k
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Help
![Transcription:
(a) Place the following in increasing order (from smallest to largest). You do not need to give explanations.
\[ A = \sum_{k=100}^{\infty} \frac{1}{2^k + 3k} \]
\[ B = \sum_{k=1}^{\infty} \frac{1}{2^k + 3k} \]
\[ C = 3 \]
\[ D = \sum_{k=1}^{\infty} \frac{1}{2^k} \]
\[ E = \sum_{k=1000}^{\infty} \frac{1}{3^k} \]
Explanation:
The problem asks to rank five mathematical expressions in increasing order of their values. The expressions involve infinite sums and a constant:
- Expression A and B are sums starting from different indices, \( k = 100 \) and \( k = 1 \), respectively.
- Expression C is a constant, 3.
- Expression D is a sum that starts from \( k = 1 \) involving powers of 2 in the denominator.
- Expression E is a sum starting from \( k = 1000 \) involving powers of 3 in the denominator.
Students are expected to evaluate or compare these expressions to order them from the smallest to largest without providing detailed explanations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3b47e7c-f6ee-4dde-9ef1-0f8b8a2d2829%2F9b4b96cc-5eee-4aa4-821d-b2bcd325834a%2F5sayjzm_processed.png&w=3840&q=75)
Transcribed Image Text:Transcription:
(a) Place the following in increasing order (from smallest to largest). You do not need to give explanations.
\[ A = \sum_{k=100}^{\infty} \frac{1}{2^k + 3k} \]
\[ B = \sum_{k=1}^{\infty} \frac{1}{2^k + 3k} \]
\[ C = 3 \]
\[ D = \sum_{k=1}^{\infty} \frac{1}{2^k} \]
\[ E = \sum_{k=1000}^{\infty} \frac{1}{3^k} \]
Explanation:
The problem asks to rank five mathematical expressions in increasing order of their values. The expressions involve infinite sums and a constant:
- Expression A and B are sums starting from different indices, \( k = 100 \) and \( k = 1 \), respectively.
- Expression C is a constant, 3.
- Expression D is a sum that starts from \( k = 1 \) involving powers of 2 in the denominator.
- Expression E is a sum starting from \( k = 1000 \) involving powers of 3 in the denominator.
Students are expected to evaluate or compare these expressions to order them from the smallest to largest without providing detailed explanations.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
