Ruby - 54 chars
def a()p=0;1000000.times{|i|p+=8/(4i(4*i+2))};p;end;
def a()p=0;1000000.times{|i|p+=8/(4*i*(4*i+2))};p;end;
My first try on console
def a()i=1;p=0;while i<2**100 do p+=8/(i*(i+2));i+=4;end;p;end;
def a()i=1;p=0;while i<2**100 do p+=8/(i*(i+2));i+=4;end;p;end;
63 chars.