Reducing Leibniz perl code in characters

Question

This Perl code is supposed to calculate the Leibniz formula. The original problem is here.

The input format is:

T
<T test cases, each on their own line>

Each test case is a number < 10^7. The output format should be the same, minus the first line.

For example, an input:

2 
10 
20

And for output:

0.760459904732351
0.77290595166696

My first solutions, at 62 and 61 characters respectively.

for(1..<>){$s=0;map{$s+=($_&1||-1)/(2*$_-1)}1..<>;print"$s\n"}

for(1..<>){$s=0;$s+=($_&1||-1)/(2*$_-1)for 1..<>;print"$s\n"}

Edit: The best solution so far is 53 characters, by @teebee:

<>;print${\map$a-=(-1)**$_/(2*$_-1),1..$_},$a=$/for<>

Answer 1

Perl 53 bytes

You can save two more strokes:

<>;print${\map$a-=(-1)**$_/(2*$_-1),1..$_},$a=$/for<>

Answer 2

Perl 55 bytes

<>;map($s-=(-1)**$_/(2*$_-1),1..$_),$s=!print$s,$/for<>

Without using any Perl non-standard features (such as say). 3 bytes are wasted removing the first value from the input.

Sample usage:

in.dat

2
10
20

$ perl leibniz.pl < in.dat
0.760459904732351
0.77290595166696

---

Alternative, also 55 bytes

map{$s-=(-1)**$_/($_*2-1)for 1..<>;$s=!print$s,$/}1..<>

The alternative may be run interactively, without requiring an input file. Which, as I understand, is what you meant by running indefinitely.