I'm confused with the Algebra, how did we get 1-2^n? I thought the 2^n both canceled out. The image contains two mathematical expressions that are explanations of sequences and their behavior.1. The first expression is:\[ a_{n+1} - a_n = \frac{n+1}{4n+3} - \frac{n}{4n-1} = \frac{1}{(4n-1)(4n+3)} < 0 \text{ for } n \geq 1, \text{ so strictly decreasing}. \]This expression demonstrates that the difference between consecutive terms of a sequence \(a_n\) is negative, indicating the sequence is strictly decreasing for \(n \geq 1\).2. The second expression is:\[ a_{n+1} - a_n = (n+1 - 2^{n+1}) - (n - 2^n) = 1 - 2^n < 0 \text{ for } n \geq 1, \text{ so strictly decreasing}. \]This indicates that for the sequence defined in this manner, the difference between consecutive terms is also negative, confirming the sequence is strictly decreasing for \(n \geq 1\).There are no graphs or diagrams in the image. The image contains a mathematical expression with its simplification steps and a note querying a step in the process. Here is the transcription:1. Original Expression: \[ (n + 1 - 2^{n+1}) - (n - 2^n) \]2. Simplified Step 1: \[ n + 1 - 2^{n+1} - n + 2^n \]3. Simplified Step 2: \[ 1 - 2^n \cdot 2^1 + 2^n \]4. Final Simplified Expression: \[ 1 - 2^n \]5. Note written beside the final expression: - "What happened that gave us \(1 - 2^n\)? I thought they canceled?"This transcription highlights the simplification of a nested expression and a query regarding the cancellation of terms, leading to the final result.

Answered: I'm confused with the Algebra, how did…

I'm confused with the Algebra, how did we get 1-2^n? I thought the 2^n both canceled out

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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