Comment by foxes

  let y=3n*(10n**1000020n);
  const f=(i,x,p)=>{(x>0)?f(i+2n,x*i/((i+1n)*4n),p+x/(i+2n)):p/(10n**20n)} 
  console.log(f(1n,y/8n,y));

Not sure if I can golf it anymore