SOLUTION: Find the sum 1+ 1/2+1/4+...+1/1024 an=1+(n-1) ^ -1/2

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Question 248545: Find the sum 1+ 1/2+1/4+...+1/1024
an=1+(n-1) ^ -1/2
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(1/2)/1=1/2
(1/4)/(1/2)=1/2
r=1/2 Geometric sequence.
a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29
(1/2)^(n-1)=1/1024
log[1/2]((1/2)^n-1)=log[1/2](1/1024) Finding n
n-1=10
n=11
S%5B11%5D=a%5B1%5D%28%281-r%5En%29%2F%281-r%29%29 Sum of a finite geometric sequence.
=1%28%281-%281%2F2%29%5E11%29%2F%281-%281%2F2%29%29%29
=.9995/.5
=1.999... the sum