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

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Homework Help Overview

The problem involves summing a geometric progression with a common ratio of √2/2. The original poster is tasked with finding the difference between the sum of the first ten terms and the sum to infinity, given specific values for the first term and common ratio.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definitions of the first term and common ratio, and whether the sums can be calculated using a single equation or if they need to be derived separately. There is also a clarification on the nature of the series as a geometric progression.

Discussion Status

The discussion is ongoing, with participants providing clarifications and confirming the nature of the series. Some guidance has been offered regarding the formulas for the sums of geometric series, but no consensus or resolution has been reached yet.

Contextual Notes

The original poster expressed confusion regarding the calculations and the equations needed for the problem. There was an acknowledgment of the need for clearer definitions and specifications in the problem statement.

zebra1707
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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?
 
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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
[tex]S_f=a\frac{1-r^n}{1-r}[/tex]

The sum of infinite numbers of geometric series
[tex]s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}.[/tex]
 
It would have been a good idea to say that this is a geometric series! Given that, njama is correct.
 
Many thanks for your replies. You have clarified my thoughts.

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

Cheers Petra d.
 

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