Find all the values of x such that the given series would converge. 9" (2")(п + 1) (n + 3) n=1 The series is convergent from x = left end included (enter Y or N): to x right end included (enter Y or N):

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem Statement:**

Find all the values of \( x \) such that the given series would converge.

\[
\sum_{n=1}^{\infty} \frac{9^n (x^n)(n+1)}{(n+3)}
\]

**Convergence Analysis:**

The series is convergent 

- from \( x = \) [______], left end included (enter Y or N): [______]
- to \( x = \) [______], right end included (enter Y or N): [______]

**Instructions:**

Determine the range of \( x \) for which the series converges and specify whether the interval endpoints are included.
Transcribed Image Text:**Problem Statement:** Find all the values of \( x \) such that the given series would converge. \[ \sum_{n=1}^{\infty} \frac{9^n (x^n)(n+1)}{(n+3)} \] **Convergence Analysis:** The series is convergent - from \( x = \) [______], left end included (enter Y or N): [______] - to \( x = \) [______], right end included (enter Y or N): [______] **Instructions:** Determine the range of \( x \) for which the series converges and specify whether the interval endpoints are included.
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