- Thread starter
- #1

#### ATroelstein

##### New member

- Jun 30, 2012

- 15

$$

\sum_{k=2}^{n}a^{n-k}

$$

I am trying to find a general formula for this summation, which turns out to be a geometric series with a as the common ratio. I have worked out the following:

$$

\sum_{k=2}^{n}a^{n-k} = \sum_{k=0}^{n-2}a^{k}

$$

$$

a^{0} + a^{1} + a^{2} + ... + a^{n-3} + a^{n-2}

$$

Plugging this information into the geometric series summation formula where the common ratio = a, the first term is 1 and the number of terms is n-2, I get:

$$

S_{n-2} = 1 * (\frac{1-a^{n-2}}{1-a})

$$

After testing this formula few times, I found that it's always slightly off. I'm wondering where I went wrong when trying to determine the formula. Thanks.