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

[Peter G.]

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: log_0.2 9.8 * 10^-6

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

Any help?

Thanks,
Peter G.

 

[Peter G.]

Never mind, sorry, spotted the mistake already!