Summing Geometric Progressions with a Common Ratio of √2/2

[zebra1707]

Homework Statement

Hi there, question asks "What is the difference between the sum to ten terms and the sum to infinity. a = sqroot 2 r = sqroot 2/2

The sum to ten terms, I worked out as 31 + 31 sqroot 2
The sum to infinity, I worked out as 2 sqroot 2 + 2

Homework Equations

Is there one equation to cover this type of problem or do I need to subtract one equation from the other to get one equation and hence one answer?

The Attempt at a Solution

Totally confused?

 

[njama]

And what are those a and r?

Is a the first term of the series, and r the common ratio?

If so, the sum to n numbers of geometric series
$$S_f=a\frac{1-r^n}{1-r}$$

The sum of infinite numbers of geometric series
$$s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}.$$

 

[HallsofIvy]

It would have been a good idea to say that this is a geometric series! Given that, njama is correct.

 

[zebra1707]

Many thanks for your replies. You have clarified my thoughts.

Yes, my apologies I should have specified a G.P.

Cheers Petra d.