SOLUTION: find the sum: (1-square root 2)^0 + (1-square root 2)^1 + (1-square root 2)^2 + ...

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Question 82095This question is from textbook
: find the sum: (1-square root 2)^0 + (1-square root 2)^1 + (1-square root 2)^2 + ...This question is from textbook

Answer by funmath(2873) About Me  (Show Source):
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find the sum: (1-square root 2)^0 + (1-square root 2)^1 + (1-square root 2)^2 + ...
The sum of an infinite series is found with the formula:highlight%28S=a%2F%281-r%29%29, where S=sum, a=first term, and r=common ratio
In this case, a=1 because anything to the 0 power is 1
r=(1-square root 2)
S=1%2F%281-%281-sqrt%282%29%29%29
S=1%2F%281-1%2Bsqrt%282%29%29
S=1%2Fsqrt%282%29 Some teachers would want you to rationalize the denominator.
S=1%2Asqrt%282%29%2F%28sqrt%282%29%2Asqrt%282%29%29
S=sqrt%282%29%2F2
Happy Calculating!!!!