1. In this problem, you will look at the geometric series 52k+3* k=2 (a) Write the series out in . notation. (b) What is the common ratio of this geometric series? (c) Write out the nth partial sum sn in…… notation. (d) Start with the equation sn = your answer in (c), multiply both sides by the common ratio, subtract from your original equation (sn = your answer in (c)) and solve for sn. (e) Take an appropriate limit of your answer to (d) to find the sum of the geometric series > 52k+3*
1. In this problem, you will look at the geometric series 52k+3* k=2 (a) Write the series out in . notation. (b) What is the common ratio of this geometric series? (c) Write out the nth partial sum sn in…… notation. (d) Start with the equation sn = your answer in (c), multiply both sides by the common ratio, subtract from your original equation (sn = your answer in (c)) and solve for sn. (e) Take an appropriate limit of your answer to (d) to find the sum of the geometric series > 52k+3*
Calculus: Early Transcendentals
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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![**Hour 16**
1. In this problem, you will look at the geometric series
\[
\sum_{k=2}^{\infty} \frac{3}{5^{2k+3}}.
\]
(a) Write the series out in ... notation.
(b) What is the common ratio of this geometric series?
(c) Write out the nth partial sum \( s_n \) in ... notation.
(d) Start with the equation \( s_n = \) your answer in (c), multiply both sides by the common ratio, subtract from your original equation \( (s_n = \) your answer in (c)) and solve for \( s_n \).
(e) Take an appropriate limit of your answer to (d) to find the sum of the geometric series
\[
\sum_{k=2}^{\infty} \frac{3}{5^{2k+3}}.
\]
2. Textbook 10.2 #14
3. Textbook 10.2 #18](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8b6e191-c688-4e0f-a48b-13ca4d471478%2Fae589441-e648-43cc-a3ea-3f269f7fb2a3%2Fu44xl_processed.png&w=3840&q=75)
Transcribed Image Text:**Hour 16**
1. In this problem, you will look at the geometric series
\[
\sum_{k=2}^{\infty} \frac{3}{5^{2k+3}}.
\]
(a) Write the series out in ... notation.
(b) What is the common ratio of this geometric series?
(c) Write out the nth partial sum \( s_n \) in ... notation.
(d) Start with the equation \( s_n = \) your answer in (c), multiply both sides by the common ratio, subtract from your original equation \( (s_n = \) your answer in (c)) and solve for \( s_n \).
(e) Take an appropriate limit of your answer to (d) to find the sum of the geometric series
\[
\sum_{k=2}^{\infty} \frac{3}{5^{2k+3}}.
\]
2. Textbook 10.2 #14
3. Textbook 10.2 #18
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