for loop continuous sum multiplication table code

A classic example of an for cycle is a continuous summation: 1+2+3+... Plus 100. I've been talking for over an hour, but some of you can't. Do the program to have thought, some students 1 straight hit the keyboard, did not get out. So before we do this sum, we have to think about 1, so the sum is really just a continuous sum, so when the variable $i is going to be increasing by itself it's going to be summing over the previous number, so how do we sum over the previous number? We can do a split: take the number before $i as a single term, and add it to $i alone. Similarly, 100 plus the sum of the previous 99 terms, 99 plus the sum of the previous 98 terms... And so on, 2 plus the previous number, 1, so what about 1, that's 1 plus 0. When you're writing a program, you're thinking in reverse. You start with 0+1=1, then 1+2=3, then 3+3=6...

 
<?php 
/* 
*file name: 1+...+100.php 
*author: luchanghong 
*email: luchanghong@xingmo.com 
*time: 2011/5/24 
*/ 
$sum = 0; 
$str = ''; 
for($i = 0 ; $i <= 100 ; ++$i) 
{ 
echo $str .= $i.'+'; 
// echo '<br>'; 
// echo $sum.'+'.$i.'='; 
echo '='; 
echo $sum = $sum+$i; 
echo '<br>'; 
} 
echo $sum; 
?> 

The echo statement in the middle of the loop body is for testing the procedure and can be seen more clearly.
The Times table 99 below USES a two-layer for cycle, which may be difficult for beginners, but you can still understand it with patience and concentration.

 
<?php 
/* 
*file name: 99.php 
*author: luchanghong 
*email: luchanghong@xingmo.com 
*time: 2011/5/9 
*/ 
echo '<table border=1>'; 
for($i = 1 ; $i<10 ; ++$i) 
{ 
echo '<tr>'; 
for($j = 1 ; $j<= $i ; ++$j) 
{ 
echo '<td>'.$j.'x'.$i.'='.$j*$i.'</td>'; 
} 
echo '</tr>'; 
} 
echo '</table>'; 
?>