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

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SUMMARY

The discussion focuses on calculating the number of terms required in an infinite summation series to achieve a difference of 0.00001. The first term is 10, and the common ratio is 0.02. The equation used is (U1 - r) / (1-r) - (U1(rn-1)) / (r - 1) = 0.00001. The correct answer for the number of terms needed is definitively 4, as identified by the participant Peter G. after correcting his initial calculations.

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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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