Prove that (1+x)^n greater than or equal to (1+nx), for all natural number n, where x -1 - Maths - Principle of Mathematical Induction

Question

Prove that (1+x)^n greater than or equal to (1+nx), for all natural
number n, where x > -1 I did not understand where the kx^2 went
(last step) in the answers given by the experts EXPERTS PLEASE
HELP​

Ghanshyam Dhakar · Accepted Answer

Dear student,
expansion of 1+xn = 1+nx +nn-12!x2 
for -1<x<1ignore x2 and higher order term then1+xn ≃ 1+nxfor x≥1then 1+xn ≥ 1+nx becouse  x2 and higher order term have contribution so 1+xn ≥ 1+nx  
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Prove that (1+x)^n greater than or equal to (1+nx), for all natural number n, where x > -1. I did not understand where the kx^2 went (last step) in the answers given by the experts. EXPERTS PLEASE HELP​

Prove that (1+x)^n greater than or equal to (1+nx), for all natural number n, where x > -1. I did not understand where the kx^2 went (last step) in the answers given by the experts. EXPERTS PLEASE HELP