This is a geometric alternating sereis with first term, a = 1 and the common ratio,r is `(-1/10)` .
Sum of first n terms is,
`S_n = a(1-r^n)/(1-r)`
`S_oo = a/(1-r)`
`S_n = 1(1-(-1/10)^n)/(1-(-1/10)) = (10/11)(1-(-1/10)^n)`
`S_oo=1/(1-(-1/10)) = 10/11 `
|S_oo-S_n| <=0.0001
|10/11 - (10/11)(1-(-1/10)^n)| <= 0.0001
10/11|1-(1-(-1/10)^n)|<=0.0001
|(-1/10)^n|<=0.00011
If n is even then,
(-1/10)^n <=0.00011
(1/10)^n <= 0.00011
n log 0.1 <= log0.00011
n (-2.3025)<= -9.1150
n=> 3.95. Therefore n must be greater than or equal to 4.
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