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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- Aug 31st 2011, 08:41 AMveronicak5678Closed 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?

- Aug 31st 2011, 10:05 AMProve ItRe: Closed Expression for Series
You have $\displaystyle \displaystyle 1 + \sum_{k = 1}^n{\frac{1}{2^{k-1}}} = 1 + \sum_{k = 1}^n{\left(\frac{1}{2}\right)^{k - 1}}$

This sum is an infinite geometric series with $\displaystyle \displaystyle a = 1, r = \frac{1}{2}$. Since $\displaystyle \displaystyle |r| < 1$, the sum is equal to $\displaystyle \displaystyle \frac{a}{1 - r}$. Go from here. - Aug 31st 2011, 10:45 AMveronicak5678Re: Closed Expression for Series
I thought that formula was for infinite series only? Can I use it if I go from 1 to n?

- Aug 31st 2011, 10:54 AMPlatoRe: Closed Expression for Series
- Aug 31st 2011, 10:55 AMProve ItRe: Closed Expression for Series
- Aug 31st 2011, 11:07 AMveronicak5678Re: Closed Expression for Series
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?

- Aug 31st 2011, 11:10 AMProve ItRe: Closed Expression for Series
- Aug 31st 2011, 01:23 PMveronicak5678Re: Closed Expression for Series
OK. Thanks to all for helping.