jumlah deret geometri tak hingga akar2 + 1 + 1/2akar2 + 1/2 ... adalah ...

[tex] \sqrt{2}+1+ \frac{1}{2} \sqrt{2} +\frac{1}{2}+... \\ a= \sqrt{2} \\ r= \frac{1}{ \sqrt{2} } . \frac{ \sqrt{2} }{ \sqrt{2} } =\frac{1}{2} \sqrt{2} \\ S_\infty = \frac{a}{1-r} = \frac{ \sqrt{2}}{1-\frac{1}{2} \sqrt{2} } . \frac{2}{2} \\ = \frac{2 \sqrt{2} }{2- \sqrt{2} } . \frac{2+ \sqrt{2}}{2+ \sqrt{2}} \\ = \frac{2\sqrt{2}(2+ \sqrt{2})}{4-2} \\ =\sqrt{2} (2+ \sqrt{2}) \\ =2 \sqrt{2+2} [/tex]
semoga membantu ya ^_^