The sum of a sequence of odd numbers gives you the sequence for the perfect squares

Really? We can test with a simple PHP Code:

<?php

echo '<h1>The sum of a sequence of odd numbers gives you the sequence for the perfect squares</h1>';

//The limit
$limit=1000;

$odd=array();

for ($i=1;$i<$limit;$i++) {

    if ($i%2!=0) {
        $odd[]=$i;
    }

}

$begin=0;
$end=1;

while ($end<count($odd)) {

    $write='';
    $result=0;

    for ($i=$begin;$i<$end;$i++) {

        $result=$result+$odd[$i];

        $write.=$odd[$i];

        if ($i==($end-1)) {
            $write.='=';
        } else {
            $write.='+';
        }

    }

    $write.=$result;

    echo '<h3>' . $write;

    $square=sqrt($result);

    if ($square==$end) {
        $question="Yes";
    } else {
        $question="No";
    }

    echo ' numbers=' . $end . ' sqrt(' . $result . ')=' . $square . ' Really? ' . $question . '</h3>';

    $end++;

}

?>