oblicz sumę szeregu geometrycznego [latex]1 + frac{ sqrt{2} }{2} + frac{1}{2} + ...[/latex]

[latex]a_1=1\q=frac{sqrt{2}}{2}=frac{1}{sqrt{2}}[/latex] [latex]S=frac{a_1}{1-q}\S=frac{1}{1-frac{1}{sqrt{2}}}=frac{sqrt{2}}{sqrt{2}-1}[/latex] [latex]S=frac{sqrt{2}(sqrt{2}+1)}{2-1}\S=2+sqrt{2}[/latex]