Question 82095
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(S=a/(1-r))}}}, 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/(1-(1-sqrt(2)))}}}
{{{S=1/(1-1+sqrt(2))}}}
{{{S=1/sqrt(2)}}}  Some teachers would want you to rationalize the denominator.
{{{S=1*sqrt(2)/(sqrt(2)*sqrt(2))}}}
{{{S=sqrt(2)/2}}}
Happy Calculating!!!!