document.write( "Question 550089: prove that if k>1 then k^n→∞ an n→∞\r
\n" ); document.write( "\n" ); document.write( "there is a hint given. Hint:let k=1+t where t>0 and use the fact that (1+t)^n>1+nt\r
\n" ); document.write( "\n" ); document.write( "prove that if k is between 0 and 1 then k^n tends to 0 as n tends to infinity \n" ); document.write( "

Algebra.Com's Answer #358405 by richard1234(7193) $\"\"$ $\"About$

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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. \n" ); document.write( "

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