$($This is from Review Exercise R$4\mathrm{.}1$ at the end of Chapter $4$ of Java for Everyone.$)$

Assume variables SimpleWriter out and int $n$ are already declared in each case. Write a separate while loop for each of the following tasks:

a$.$ Print all squares less than $n.$ For example, if $n$ is $100,$ print $0149162536496481.{?}_{?}$

b$.$ Print all positive numbers that are divisible by $10$ and less than $n.$ For example, if $n$ is $100,$ print ${102030405060708090}_{?}.$

c$.$ Print all powers of two less than $n.$ For example, if $n$ is $100,$ print $1248163264.$

$($The first four of these are from Review Exercise R$4\mathrm{.}3$ at the end of Chapter $4$ of Java for Everyone$).$ Using the kind of tracing tables discussed in Writing and Tracing Loops, provide tracing tables for these loops:

a$.$

b$.$

c$.$

d$.$

e$.$

$($This is from Review Exercise R$4\mathrm{.}15$ at the end of Chapter $4$ of Java for Everyone.$)$ Rewrite the following for loop into a while loop.

Given variables int $n$ and double pi$,$ write a snippet of code that assigns to pi the approximation of $$ resulting from adding the first $n$ terms in the Gregory$-$Leibniz series:

$=4{\displaystyle \underset{i=0}{\overset{}{}}}\frac{(-1{)}^i}{2i+1}=4(\frac{1}{1}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+$dots$)$

Given variables int areaBound and int sum, write a snippet of code that assigns to sum the result of adding up all integers of the form $n^2+m^2$ where:

@ both $n$ and $m$ are at least $1,$ and

@$n^2$ areaBound, and

@$m^2$ areaBound $.$

Additional Questions

Modify the loop to approximate pi with the Gregory$-$Leibniz series so that, instead of adding a given number of terms, it keeps adding terms until the difference between two consecutive estimates is less than some predefined tolerance, say double epsilon $=0\mathrm{.}0001.$