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Finished and Deleted

Guest Sep 18, 2018
edited by Guest  Sep 19, 2018
 #1
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I think this reads

 

\(x \geq -1,~\text{ Prove using induction that }(1+x)^n \geq 1+nx\)

 

\(P_1 = (1+x)^1 \geq 1+(1)x \\ \\ P_1 = (1+x) \geq (1+x) = TRUE\)

 

\(\text{Assume }P_n \text{ is TRUE} \\ \\ (1+x)^{n+1} = (1+x)^n(1+x) \geq (1+n x)(1+x) =\\ 1+(n+1)x+nx^2 \geq 1+(n+1)x \\ \\ \text{Thus }P_n \Rightarrow P_{n+1} \bigtriangleup\)

Rom  Sep 18, 2018
 #2
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THANKS SO MUCH!!!

Guest Sep 19, 2018

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