Geometric Series starting from 1

[seal308]

My textbook has this formula:

I have a question that has a geometric series that starts from 1, how do I solve that.
Specifically this:

My attempt was this:

But I don't get how this would change the formula on the right hand side

 

[seal308]

Not sure what you're asking.

Standard formula for geometric series:
SUM = a(m^n - 1) / (m - 1)
a = 1st term
m = multiplyer
n = number of terms.

Example: 1,3,9,27 = 40
a=1, m=3, n=4
SUM = 1(3^4 - 1) / (3 - 1) = 40

Does that help?

It's alright I found my book has the formula for a geometric series starting from 0. So I got the solution.

 

[Deleted member 4993]

My textbook has this formula:

I have a question that has a geometric series that starts from 1, how do I solve that.
Specifically this:

My attempt was this:

But I don't get how this would change the formula on the right hand side

That series

does not start with 1.

It goes like → a*r + a*r² + a*r³ + a*r⁴ ..... + a*r^n-1 + a*rⁿ

Is that what you wanted?

 

[seal308]

Huh?
0 * 3 = 0 * 3 = 0 * 3 = 0......

This:

 

[mmm4444bot]

If the first term is 0, then any SUM will equal 0.
Why apply a formula?

seal308 misspoke, when posting that the series starts with zero. The index starts at zero.