Thread: Closed Expression for Series

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?

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.