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4

Part of 2011 Hanoi Open Mathematics Competitions

Problems(2)

4 statements on real, how many correct? (HOMC 2011 J Q4)

Source:

7/25/2019
Among the five statements on real numbers below, how many of them are correct? "If a<b<0a < b < 0 then a<b2a < b^2" , "If 0<a<b0 < a < b then a<b2a < b^2", "If a3<b3a^3 < b^3 then a<ba < b", "If a2<b2a^2 < b^2 then a<ba < b", "If ∣a∣<∣b∣|a| < |b| then a<ba < b",
(A) 00, (B) 11, (C) 22, (D) 33, (E) 44
algebrainequalities
1 + x + x^2 + x^3 + ...+ x^{2011} &gt;=0 for x&gt;=-1 (HOMC 2011 Q4)

Source:

7/25/2019
Prove that 1+x+x2+x3+...+x2011≥01 + x + x^2 + x^3 + ...+ x^{2011} \ge 0 for every x≥−1x \ge - 1 .
algebrainequalitiespolynomial