Find the decimal form of 1/5+1/5²+1/5³
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Because the first term is 1, it will converge to 1.25. Even if you remove the first term, the rest of it will still converge to 1/4 because of the new first term of 1/5. if you remove 1/5 as the first term, it will still converge to 1/20 because of the new first term of 1/25…….etc. Therefore, you have to re-write your sequence in some other way.
Step-by-step explanation:
The sum to infinity is S = 1/(1–(1/5)) = 5/4
The sum of n terms is,
s = ( 1 - (1/5)^n )/ ( 1 - (1/5) )
s = (5/4) ( 1 - (0.8)^n )
We want,
S - s < 10^(-6)
s > S - 10^(-6)
I think the answer comes out to be n >= 8
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