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Ch 185: Single Variable Calculus II (Sp24)- Online > Assessment omework for Section 6.2: Properties of Power Series ore: 11/13 11/13 answered • Question 8 Textbook < > @Videos [+] Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. $\sum_{n=1}^{\infty} \frac{n}{9^n}$ Hint: Write it as $f'(\frac{1}{9})$ where $f(x) = \sum_{n=0}^{\infty} x^n$. Question Help: Post to forum Submit Question

          Ch 185: Single Variable Calculus II (Sp24)- Online > Assessment
 omework for Section 6.2: Properties of Power Series
ore: 11/13 11/13 answered
• Question 8
Textbook
< >
@Videos [+]
Evaluate the infinite series by identifying it as the value of a derivative of a geometric series.
$\sum_{n=1}^{\infty} \frac{n}{9^n}$
Hint: Write it as $f'(\frac{1}{9})$ where $f(x) = \sum_{n=0}^{\infty} x^n$.
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Ch 185: Single Variable Calculus II (Sp24)- Online > Assessment
omework for Section 6.2: Properties of Power Series
ore: 11/13 11/13 answered
• Question 8
Textbook
< >
@Videos [+]
Evaluate the infinite series by identifying it as the value of a derivative of a geometric series.
∑n=1^∞(n)/(9^n)
Hint: Write it as f'((1)/(9)) where f(x) = ∑n=0^∞ x^n.
Question Help: Post to forum
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Added by Christopher F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/17/2022

Step 1

The sum of this series is given by the formula for the sum of an infinite geometric series: S = a / (1 - r), where a is the first term and r is the common ratio. In this case, a = 1 and r = x, so f(x) = 1 / (1 - x). Show more…

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h 185: Single Variable Calculus II (Sp24)- Online > Assessment omework for Section 6.2: Properties of Power Series ore: (11)/(13),(11)/(13) answered Question 8 Textbook Videos ^(-5)[+] Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. sum_(n=1)^(infty ) (n)/(9^(n))= Hint: Write it as f^(')((1)/(9)) where f(x)=sum_(n=0)^(infty ) x^(n). Question Help: Post to forum 185:Single Variable Calculus II(Sp24-Online>Assessment omework for Section 6.2:Properties of Power Series ore11/1311/13answered O Question 8 Textbook Videos [+] Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. iM8 n 9n Hint: Write it as f' where fx Question Help:Post to forum Submit Question