Joining array elements with no separator
Use the -join operator...
$array -join ''
...or the static String.Join method...
[String]::Join('', $array)
...or the static String.Concat method...
[String]::Concat($array)
For all of the above the result will be a new [String] instance with each element in $array concatenated together.
Fixing the for loop
Your for loop will output each element of $array individually, which will be rendered on separate lines. To fix this you can use Write-Host to write to the console, passing -NoNewline to keep the output of each iteration all on one line...
for ($i = 0; $i -lt $array.Length; $i++)
{
Write-Host -NoNewline $array[$i]
}
Write-Host
The additional invocation of Write-Host moves to a new line after the last array element is output.
If it's not console output but a new [String] instance you want you can concatenate the elements yourself in a loop...
$result = ''
for ($i = 0; $i -lt $array.Length; $i++)
{
$result += $array[$i]
}
The += operator will produce a new intermediate [String] instance for each iteration of the loop where $array[$i] is neither $null nor empty, so a [StringBuilder] is more efficient, especially if $array.Length is large...
$initialCapacity = [Int32] ($array | Measure-Object -Property 'Length' -Sum).Sum
$resultBuilder = New-Object -TypeName 'System.Text.StringBuilder' -ArgumentList $initialCapacity
for ($i = 0; $i -lt $array.Length; $i++)
{
$resultBuilder.Append($array[$i]) | Out-Null # Suppress [StringBuilder] method returning itself
}
$result = $resultBuilder.ToString()