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

AI Thread Summary
To determine the number of terms needed for an infinite summation series with a first term of 10 and a common ratio of 0.02 to differ by 0.00001, a calculation was attempted using the formula for the sum of a geometric series. The equation set up involved the difference between the infinite sum and the finite sum of the terms. Initially, an error was made in the calculations, leading to an incorrect answer. However, the original poster, Peter G., later identified and corrected the mistake, ultimately confirming that the correct number of terms required is 4. This highlights the importance of careful calculation in solving problems related to infinite series.
Peter G.
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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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Never mind, sorry, spotted the mistake already!
 
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