p$01$ Series approximations

Use the cmd p$01$fig $=$ figure; to create a figure for problem p$01$ that has a $22$ tiledlayout with $4$ plots as shown below.

Refer to the example code.

Make sure the tiledlayout title matches the example but with your

username@calpoly.edu

Use the nexttile cmd for each plot

Use the text cmd to place text on each plot that matches the example

Use the grid on; cmd if needed for plots that have a grid in the example output

Make sure each plot has matching linestyle and color

Make sure each plot has matching $x$ and $y$ limits

Make sure each plot has matching $x$ and $y$ ticks

Make sure each plot has matching $x$ and $y$ labels

Make sure each plot title matches the example

Use format long for p$01$

p$01$a$.$ Use a while loop to calc the sum of the first $50$ terms of the following series,

$1={\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n(n+1)}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}$cdots

p$01$b$.$ Use a while loop to calc the sum of the first $50$ terms of the following series,

$ln(2)={\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^{n-1}}{n}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}$cdots

p$01$c$.$ Use a while loop to calc the sum of the first $25$ terms of the following series, $=\frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\frac{4}{11}$cdots

HINT: use $\backslash$pi for Greek symbol $$

p$01$d$.$ Use a while loop to calc the sum of the first $15$ terms of the following series,

$a^x={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(lna{)}^n}{n!}{x}^n$

where the value of $a$ is $3$ and $x$ is $2\mathrm{.}4$

HINT: use the factorial cmd for $!$

HINT: use $x=0$:$14$;

Additional Note

The last $2-$digits of p$01$d may vary, depending on your OS and processor.

For example,

p$01$d $=$

$13\mathrm{.}966608274671838\%$ That is okay.

p$02$ While loops and if elseif else statements

Figure $1$

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$0$ a

A $$

$p01a=$

$0\mathrm{.}980392156862745$

$p01b=$

$0\mathrm{.}683247160575918$

$p01c=$

$3\mathrm{.}181576685435032$

$p01d=$

$13\mathrm{.}966608274671840$