text: For n=0 the statement is false ("0>1")\nfor n=1 the statement is false too ("1>2")\nYet, for n=2 it is true: (8>4)\n\n...\n\nIf you do an empyrical investigation, you discover that the inequality is true for all n between 2 and 9 (including the extremes)\n\nHow can you prove this by induction?\n\nWrite the inequality for n+1:\n(n+1)^3 > 2^(n+1)\nDevelop the cube and the power:\nn^3 + (3n^2+3n+1) > 2*2^n (=2^n + 2^n)\nYour inequality is true until 3n^2+3n+1 > 2^n\nDraw exactly the parabola and the exponential and get your interval of truth.\n\nI hope that was what you needed.\n\np.s.\ntry it with all n >= 10 : the statement will prove itself to be false