By E I mean sum from k=1 to n Find a closed expression for 1+ E [1 / 2^(k-1)] I used the formula for geo series and have the sum = 1 - 1/2^n. Is this correct? How do I make a closed expression?
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Originally Posted by veronicak5678 By E I mean sum from k=1 to n Find a closed expression for 1+ E [1 / 2^(k-1)] I used the formula for geo series and have the sum = 1 - 1/2^n. Is this correct? How do I make a closed expression? You have This sum is an infinite geometric series with . Since , the sum is equal to . Go from here.
I thought that formula was for infinite series only? Can I use it if I go from 1 to n?
Originally Posted by veronicak5678 I thought that formula was for infinite series only? Can I use it if I go from 1 to n?
Originally Posted by veronicak5678 I thought that formula was for infinite series only? Can I use it if I go from 1 to n? Yes you are right. But there is a formula for finite geometric series as well, as Plato has explained.
Using that formula for finite series is how I came up with the expression from my first post, 1 - 1/2^n. Is this correct? Is it closed?
Originally Posted by veronicak5678 Using that formula for finite series is how I came up with the expression from my first post, 1 - 1/2^n. Is this correct? Is it closed? Yes it's correct. It's now closed because it is not a sum depending on k, it is a single value.
OK. Thanks to all for helping.
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