SOLUTION: 1/2 +1/8 +1/32 +...+1/2^2n-1 Need to find the limit. Please help.

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Question 1201544: 1/2 +1/8 +1/32 +...+1/2^2n-1
Need to find the limit. Please help.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

You have a geometric progression with the 1st term a = 1/2 and the common ratio r = 1/4.


The general formula for the sum of such progression is  S = a%2F%281-r%29,  provided |r| < 1.


Substituting a = 1/2, r = 1/4 into the formula, you get the answer to your question

    the sum = S = %28%281%2F2%29%29%2F%28%281-1%2F4%29%29 = %28%281%2F2%29%29%2F%28%283%2F4%29%29 = 4%2F%282%2A3%29 = 2%2F3.

Solved, with all necessary explanations.