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Suppose that q = 1 is a constant. Calculate the sum Sn = Ёка kq* = q + 2q² +3q³ + ... + nq" k=1

Suppose that q = 1 is a constant. Calculate the sum Sn = Ёка kq* = q + 2q² +3q³ + ... + nq" k=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem 4.4 Suppose that \( q \neq 1 \) is a constant. Calculate the sum \[ S_n = \sum_{k=1}^{n} k q^k = q + 2q^2 + 3q^3 + \cdots + n q^n \]
Transcribed Image Text:### Problem 4.4 Suppose that \( q \neq 1 \) is a constant. Calculate the sum \[ S_n = \sum_{k=1}^{n} k q^k = q + 2q^2 + 3q^3 + \cdots + n q^n \]
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