Sum of geometric series (1 Viewer)

[Shazer2]

I am trying to find the sum for this, but since the series starts at n=2 the formula isn't giving me the correct result. I've tried doing S₁₀ = (a(r^n-1))/r-1 since |r| > 1. However, I get the wrong result by a big margin. How do I evaluate questions such as this when the first term isn't 0 or 1?

 

[Drongoski]

One way to look at this is: it is the sum of the 1st 9 terms a geometric series : 1st term a = 1/5, common ratio r = 5

 

[Shazer2]

I provided the answer in the OP, so 488281/5 is the answer, but I'm not sure how to get that.

EDIT: That's right! Is that the only way to do it?

 

[Drongoski]

I presume you'd know the formula for the sum of the 1st n terms of a GP - so I used it.

 

[Shazer2]

I do, but how come you can do sum of 1-9 is = to 2-10.... will that always work?

 

[Drongoski]

Suppose you are reqd to find the sum of a GP from T₆ to T₅₅.

Isn't this the same as finding the sum of the 1st 50 terms of an equivalent geometric sequence, with the same common ratio, but whose 1st tern is th 6th term of the original one?

Or another way of looking at it: if you chop off the 1st 5 terms of a GP(old term: geometric progression), don't you have another GP? Or for that matter, remove the first 5000 terms, you still end up with another GP. But remove 1 or more terms from inside a GP,then it is no longer one.