What is the formula for finding the sum of a Geometric Series?

In summary, the conversation discusses a problem with finding the total sum of a geometric series using a formula. The formula given is not clear and the person asking for help is advised to either use proper LaTeX code or explain the problem more clearly. The conversation ends with a suggestion to use the formula for a finite geometric series, which is provided.
  • #1
ssjSolidSnake
3
0
Hi, I'm having trouble finding the sequence's total sum from a formula concerning Geometric Series.
I've been using a calculator to find and manually input all of the terms into a table in Microsoft Excel and adding them all up at the end. The formula that I was given was [tex]\overline{10}\sum\underline{1}[/tex]4(1/2)^n-1

The total sum that I found was 7.992188, but it was incorrect.

Can anyone help me find the Series Sum?
 
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  • #2
Can you express the question a little more precisely? I can't make sense of the overline 10, the underline 1, and where the rest of the formula is supposed to go. Please either use proper TeX code, or don't use it at all and write it out clearly and unambiguously. For example,
[tex]10 \sum_{n = 0}^\infty \frac{1}{4} \left( \frac{1}{2} \right)^{n - 1}[/tex]
or
10 * (sum from n = 0 to infinity)[ (1/4) (1/2)^(n - 1) ]
 
  • #3
Sorry about that. I'm not familiar with LaTex so I will attempt to state my problem as clearly as possible. (sum from n=1 to 10) [ 4(1/2)^(n - 1) ]

Thanks for the advice CompuChip
 
  • #4
It looks like you have a finite geometric series.

sum(0,N) an = (1-aN+1)/(1-a)

You should be able to do the rest
 
  • #5

1. What is a geometric series?

A geometric series is a sequence of numbers in which each term is multiplied by a common ratio to get the next term. The general formula for a geometric series is a + ar + ar^2 + ar^3 + ... + ar^n, where a is the first term and r is the common ratio.

2. How do you find the sum of a geometric series?

The formula for finding the sum of a finite geometric series is S = a(1 - r^n)/(1 - r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms. For an infinite geometric series, the sum is equal to a/(1 - r), as long as the absolute value of r is less than 1.

3. What is the difference between a finite and infinite geometric series?

A finite geometric series has a specific number of terms, while an infinite geometric series continues on forever. The sum of a finite geometric series can be calculated using a formula, but the sum of an infinite geometric series can only be calculated when the common ratio is less than 1.

4. How can geometric series be applied in real life?

Geometric series can be used to model situations that involve growth or decay, such as population growth, compound interest, or radioactive decay. They are also used in various fields of science, such as physics and biology, to describe natural phenomena.

5. What are some common mistakes when solving geometric series problems?

Some common mistakes include forgetting to check if the common ratio is less than 1 for an infinite series, using the wrong formula for the sum of a finite series, and not simplifying the final answer. It is also important to pay attention to the given information and make sure it aligns with the formula being used.

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