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OpenStudy (anonymous):
Use the principle of mathematical induction to show that: a_n = n/(n^2 + 1) is decreasing. BASE CASE: Show that n = 1 is true. I did this INDUCTION HYPOTHESIS Assume n = k is true => a_k < a_k+1 => (k)/(k^2 + 1) < (k+1)/((k+1)^2 + 1) a_k = (k)/(k^2 + 1) SHOW: Show that n = k + 1 is true: => a_k+1 < a_k+2 => (k+1)/((k+1)^2 + 1) < (k+2)/((k+2)^2 + 1) I am stuck on this induction step. How do I "revive" the a_k expression on my LHS or RHS of the above expresion?
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OpenStudy (anonymous):
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