Summing up the Infinite: 3(1/11)^n

  • Thread starter Lance WIlliam
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In summary, the formula for "Summing up the Infinite: 3(1/11)^n" is 3 multiplied by the infinite geometric series with a common ratio of 1/11. To solve for the sum of this infinite series, you can use the formula S = a/(1-r), where S is the sum, a is the first term, and r is the common ratio. The sum of this infinite series is finite, meaning it has a specific numerical value. The value of the sum of "Summing up the Infinite: 3(1/11)^n" is 33/10 or 3.3. This can be calculated by plugging in the values for a and r in the formula
  • #1
Lance WIlliam
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[tex]\sum[/tex] as n=0(theres a infinity above that sigma) , 3(1/11)^n

I thought it would just be 3/11 and converge due to the geometric test but its not...to find the sum would I just start at 0 and put numbers in for "n"...
 
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  • #2
You mean [tex]\sum^{\infty}_{n=0} 3\left(\frac{1}{11^n}\right)[/tex]. You can factor the 3 outside of the sigma. And the resulting would be a geometric series, no?
 
  • #3
yes but I don't see how I would go about finding a actual sum.
 
  • #4
What do you know about the sum of a geometric series?
 
  • #5
OH! S=a/1-r
 
  • #6
its 33/10 thankyou
 

1. What is the formula for "Summing up the Infinite: 3(1/11)^n"?

The formula for "Summing up the Infinite: 3(1/11)^n" is 3 multiplied by the infinite geometric series with a common ratio of 1/11.

2. How do you solve for the sum of this infinite series?

To solve for the sum of this infinite series, you can use the formula S = a/(1-r), where S is the sum, a is the first term, and r is the common ratio. In this case, a = 3 and r = 1/11.

3. Is the sum of this infinite series finite or infinite?

The sum of this infinite series is finite, meaning it has a specific numerical value. It does not go on forever.

4. What is the value of the sum of "Summing up the Infinite: 3(1/11)^n"?

The value of the sum of "Summing up the Infinite: 3(1/11)^n" is 33/10 or 3.3. This can be calculated by plugging in the values for a and r in the formula S = a/(1-r).

5. What are the practical applications of this infinite series?

This infinite series can be used in various fields such as finance, physics, and engineering to calculate compound interest, decay rates, and growth patterns. It can also help in understanding the concept of infinity and its implications in mathematics.

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