how do i show that the statement hold for every positive integer n using induction? (1+ n)2 ≥ 3n + 1
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Originally Posted by polymerase how do i show that the statement hold for every positive integer n using induction? (1+ n)2 ≥ 3n + 1 I assume you mean, $\displaystyle (n+1)^2 \geq 3n+1$ It is true for $\displaystyle n=1$. Assume it is true for $\displaystyle n=k$ that is, $\displaystyle (k+1)^2 \geq 3k+1$ Then, $\displaystyle (k+2)^2 = k^2+4k+4 = (k^2+2k+1)+(2k+2)\geq 3k+1 + 3 = 3(k+1)+1$
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