Data Sufficiency

nidhis.1408 wrote:Is 1+x+x^2+...+x^10 positive?
(1) x<−1
(2) x^2 > 2

Please help me with this problem.

Sum of first n terms of a geometric progression is, S = a(r^n - 1)/(r - 1), where a = first term, r = common ratio, which is not equal to 1, and n = number of terms
Now in this case if we take a = 1, r = x, and n = 11, then
Sum = (x^11 - 1)/(x - 1)

(1) x < -1 implies (x^11 - 1)/(x - 1) = negative/negative = positive; SUFFICIENT.

(2) x² > 2 implies either x > √2 or x < -√2
If x > √2, then (x^11 - 1)/(x - 1) = positive/positive = positive
If x < -√2, then (x^11 - 1)/(x - 1) = negative/negative = positive; SUFFICIENT.

The correct answer is D.