# SOLUTION: prove that if k>1 then k^n&#8594;&#8734; an n&#8594;&#8734; there is a hint given. Hint:let k=1+t where t>0 and use the fact that (1+t)^n>1+nt prove that if k is between 0 an

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: prove that if k>1 then k^n&#8594;&#8734; an n&#8594;&#8734; there is a hint given. Hint:let k=1+t where t>0 and use the fact that (1+t)^n>1+nt prove that if k is between 0 an      Log On

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 Click here to see ALL problems on Sequences-and-series Question 550089: prove that if k>1 then k^n→∞ an n→∞ there is a hint given. Hint:let k=1+t where t>0 and use the fact that (1+t)^n>1+nt prove that if k is between 0 and 1 then k^n tends to 0 as n tends to infinityAnswer by richard1234(5390)   (Show Source): You can put this solution on YOUR website!Given the hint, the problem becomes simple. Since 1 + nt approaches infinity as n approaches infinity, the LHS of the inequality is "bounded" by this expression, so the LHS must also approach infinity.