Let r = 17. For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise. A. Consider the sequence {nr"}. lim nr" = 12-00 B. Take my word for it that can be shown that Now consider the series n=1 nr." = n=1 nr i=1 'ir² = nrn+2 (n + 1)²+1 + r (1 — r)²
Let r = 17. For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise. A. Consider the sequence {nr"}. lim nr" = 12-00 B. Take my word for it that can be shown that Now consider the series n=1 nr." = n=1 nr i=1 'ir² = nrn+2 (n + 1)²+1 + r (1 — r)²
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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![Let \( r = \frac{17}{24} \).
For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.
A. Consider the sequence \(\{nr^n\}\).
\[
\lim_{n \to \infty} nr^n = \_\_\_
\]
B. Take my word for it that it can be shown that
\[
\sum_{i=1}^n ir^i = \frac{nr^{n+2} - (n+1)r^{n+1} + r}{(1-r)^2}.
\]
Now consider the series \(\sum_{n=1}^\infty nr^n\).
\[
\sum_{n=1}^\infty nr^n = \_\_\_
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccac55ee-732b-4607-a38e-f5bd0a8aacb2%2Fec1b1c7e-59b6-4f71-93ed-9b88867fd527%2F6pyb25u_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( r = \frac{17}{24} \).
For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.
A. Consider the sequence \(\{nr^n\}\).
\[
\lim_{n \to \infty} nr^n = \_\_\_
\]
B. Take my word for it that it can be shown that
\[
\sum_{i=1}^n ir^i = \frac{nr^{n+2} - (n+1)r^{n+1} + r}{(1-r)^2}.
\]
Now consider the series \(\sum_{n=1}^\infty nr^n\).
\[
\sum_{n=1}^\infty nr^n = \_\_\_
\]
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