Solve this with step by step explanation so i understand better. YEARDATE MONTH5: Find a Sequencex which is in with P>lbutL'.Sole-

Answered: O Find but Sequence x which isin lľ…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Solve this with step by step explanation so i understand better.

YEAR
DATE MONTH
5: Find a Sequence
x which is in with P>l
but
L'.
Sole-

Expert Solution

Step 1

The objective is to find the sequence which is in $l^{p}$ for $p > 1$ but not in $l^{1}$ .

The $l^{p}$ space is defined as for the sequence $a_{n}$ if the series,

$\sum_{n = 1}^{\infty} {|a_{n}|}^{p} < \infty$

The sequence exist,

Let's take $x = \sum_{n = 1}^{\infty} a_{n}$

where $a_{n} = \frac{1}{n}$

The series does not converge by p series test.

p-series test says that,

$\sum_{n = 1}^{\infty} \frac{1}{x^{p}}$ converges is $p > 1$ and diverges for $p = 1$ .

So $x \notin l^{1}$ .

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O Find but Sequence x which isin lľ with P>l. a 4 L'.