Determine the Sum of the Following Infinite Series $\sum _ { \mathrm { k } = 0 } ^ { \infty } ( 1 - \sqrt { 2 } ) ^ { \mathrm { k } }$

question 20

Short Answer

Determine the sum of the following infinite series: $\sum _ { \mathrm { k } = 0 } ^ { \infty } ( 1 - \sqrt { 2 } ) ^ { \mathrm { k } }$ .
Enter your answer exactly in the reduced form $\frac { a } { \sqrt { b } }$ .

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