# Math Help - help me to simplify this

1. ## help me to simplify this

$\sum\limits_{n = 0}^{n - 1} \left({\frac {1}{2}}\right) ^ n$

2. I assume that $n-1$ on sigma is a constant and not related to the summation.

$\sum _{k=0}^a r^k = \frac{r^{1+a}-1}{r-1}$

So,
$\sum_{n = 0}^{n - 1} \left({\frac {1}{2}}\right)^n = \frac{\left(\frac{1}{2}\right)^{1+(n-1)}-1}{\frac{1}{2}-1} = 2 - 2^{1-n}$

3. ## wel wel wel

well i think the answer to that question is 1 though im not sure

4. Originally Posted by gen2dan
well i think the answer to that question is 1 though im not sure
If it was the infinite series $\sum_{n=1}^{\infty} \left( \frac{1}{2} \right)^n$ then the answer would indeed be 1.

But it's not so it's not.

(Note: The very first term of the given series is $\left( \frac{1}{2} \right)^0 = 1$ so clearly it can't sum to 1 .......)