For the infinite geometric series $1 + \dfrac{1}{\sqrt{2}} + \dfrac{1}{2} + \dfrac{1}{2\sqrt{2}} + \ldots$, the sum to i

Question

For the infinite geometric series $1 + \dfrac{1}{\sqrt{2}} + \dfrac{1}{2} + \dfrac{1}{2\sqrt{2}} + \ldots$, the sum to infinity is —

Accepted Answer

$\dfrac{\sqrt{2}}{\sqrt{2} - 1}$

Answer

$\dfrac{1}{\sqrt{2} - 1}$

Answer

$\sqrt{2}$

Answer

$1$

For the infinite geometric series 1+12+12+122+…1 + \dfrac{1}{\sqrt{2}} + \dfrac{1}{2} + \dfrac{1}{2\sqrt{2}} + \ldots1+2​1​+21​+22​1​+…, the sum to infinity is —