Finding the sum of a geometric series

[umzung]

Homework Statement

Calculate:

Relevant Equations

The sum of 5 x 10^i, from i=0 to i=n-1

I'm using the sum of a geometric series formula, but I'm not sure how to find the ratio, r. The n is confusing me.

The solution is below, but I'm having trouble with the penultimate step.

 

[andrewkirk]

The ratio is 10. In a geometric seqence the ratio of consecutive terms is always the item that is raised to the power of the sequence index number (j in this case).

 

[WWGD]

Here r is the ratio of consecutive terms. The general term is 5x10^i ; it is indexed by i. Can you use this to find the ratio between consecutive terms?

 

[tnich]

Consider this:
$\sum_{i=0}^{n-1} ab^i = \sum_{i=0}^\infty ab^i - \sum_{i=n}^\infty ab^i$

 

[umzung]

The ratio is 10. In a geometric seqence the ratio of consecutive terms is always the item that is raised to the power of the sequence index number (j in this case).

Thanks. The formula is first term*(1-r^n)/(1-r). How does 1-r become reversed in the solution?

 

[tnich]

Try multiplying the top and bottom of the expression by -1.

 

[osilmag]

Wolfram

Wolfram Mathmatica gives a nice explanation of geometric series.