Math Help - summation problem

1. summation problem

If I am reducing the lower limit of a summation how does this work algebraically

I have this as a solution and don't know where it comes from

Summation from x=1 to infinity of (1/2*exp(t))^x

The lower limit is then reduced;

1/2*exp(t) * Summation from x=0 to infinity of (1/2*exp(t))^x

Where does the 1/2*exp(t) come from ??

I thought it was x=0 for f(x) added to the expression but that is simply 1

2. Originally Posted by revolution2000
If I am reducing the lower limit of a summation how does this work algebraically

I have this as a solution and don't know where it comes from

Summation from x=1 to infinity of (1/2*exp(t))^x

The lower limit is then reduced;

1/2*exp(t) * Summation from x=0 to infinity of (1/2*exp(t))^x

Where does the 1/2*exp(t) come from ??

I thought it was x=0 for f(x) added to the expression but that is simply 1
In general $\sum_{n=1}^N f(n) = \sum_{n=0}^{N-1}f(n+1)$ so in your case the generator becomes $\left(\frac{1}{2}e^t\right)^{x+1}$or $\frac{1}{2}e^t \left(\frac{1}{2}e^t\right)^{x}$