Which of the following result is valid?

Let P(n):    (1+x)n≥(1+nx)For n=1,    (1+x)1=1+x=1+1⋅x≥1+1⋅x     (1+x)1≥1+1⋅xFor n=k, let P(k):(1+x)k≥(1+kx) is true. For n=k+1,P(k+1):(1+x)k+1≥{1+(k+1)x} we shall show P (k + 1) is true. consider,(1+x)k+1=(1+x)k⋅(1+x)≥(1+kx)(1+x)  [ if x>−1]=1+x+kx+kx2≥1+x+kx [∵k>0 and x>−1]=1+(k+1)xThus,(1+x)k+1≥1+(k+1)x, if x>−1