How Many Terms to Achieve a Difference of 0.00001 in Infinite Summation Series?

In summary, an infinite summation series is a mathematical concept involving adding an infinite number of terms together, often represented by the symbol Σ. Its calculation involves finding the limit of partial sums, which determines whether the series is convergent (finite sum) or divergent (infinite sum). Various tests can be used to determine convergence or divergence. Real-life applications of infinite summation series can be found in fields such as physics, engineering, and economics.
  • #1
Peter G.
442
0
Hi,

First term is 10 and common ration is 0.02. We have to find the number of terms necessary so that the difference between the infinite summation and the sum of those terms differ by 0.00001.

This is what I did:

(U1 - r) / (1-r) - (U1(rn-1)) / (r - 1) = 0.00001

I get: - 0.2n + 10 = (0.00001 - 500 / 49) x (-0.98)

I then do: log0.2 9.8 * 10-6

And I don't get the right answer, which is 4.

Any help?

Thanks,
Peter G.
 
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  • #2
Never mind, sorry, spotted the mistake already!
 

1. What is an infinite summation series?

An infinite summation series is a mathematical concept that involves adding an infinite number of terms together. It is often denoted by the symbol Σ (sigma) and is used to represent the sum of a sequence of numbers. An example of an infinite sum series is the harmonic series: 1 + 1/2 + 1/3 + 1/4 + ...

2. How is an infinite summation series calculated?

The calculation of an infinite summation series involves finding the limit of the partial sums of the series. This means adding a finite number of terms from the series and then taking the limit as the number of terms approaches infinity. The value of the limit, if it exists, is the sum of the infinite series.

3. What is the difference between a convergent and a divergent infinite summation series?

A convergent infinite summation series is one whose limit of the partial sums exists and is a finite number. This means that the series has a finite sum. On the other hand, a divergent infinite summation series is one whose limit does not exist or is infinite. This means that the series does not have a finite sum.

4. How do you determine if an infinite summation series is convergent or divergent?

There are several tests that can be used to determine the convergence or divergence of an infinite summation series. These include the integral test, comparison test, ratio test, and root test. These tests involve comparing the given series to known convergent or divergent series and using mathematical operations to determine the behavior of the series.

5. What are some real-life applications of infinite summation series?

Infinite summation series have many real-life applications in various fields such as physics, engineering, and economics. For example, the concept of infinite series is used in the calculation of electric potential and capacitance in physics, and in the design of bridges and buildings in engineering. In economics, infinite series are used in the analysis of interest rates and the calculation of compound interest.

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