SOLUTION: Find the to infinity of 1+1/2+1/4+...

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Question 1054149: Find the to infinity of 1+1/2+1/4+...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is a geometric series. In this case,

first term = a = 1
common ratio = r = 1/2 = 0.5

In plain english, we start with the term 1. To get the next term, we multiply 1 by 1/2 to get 1/2. So the second term is 1/2. The third term is 1/4 since (second term)*(r) = (1/2)(1/2) = 1/4. And so on. This is continued on forever to generate an infinite number of terms. These terms are added up.

The question is: do all of the terms add up to a fixed number? Or do these terms just go on forever making the sum larger and larger?

Since r = 1/2, which is between -1 and +1, this means that the series does converge. The sum slowly gets closer and closer to a fixed value. The sum does NOT go on forever.

Let's find that infinite sum S

S+=+a%2F%281-r%29

S+=+1%2F%281-0.5%29 Plug in a = 1 and r = 0.5 (same as 1/2)

S+=+1%2F%280.5%29

S+=+2

So this means
1+1/2+1/4... = 2