Question

Let x > -1 and n being a natural number

Proove: (1+x)^n ≥ 1+nx

Answer 1

Using induction

Answer 2

n =1
we have
(1+x)^1=x+1=1+x
lets assume it is true for some k>=1
so we have (1+x)^k>=1+kx
we need to show it is true for k+1
(1+x)^(k+1)=(1+x)^k*(x+1)>=(1+kx)*(x+1)>=x+1+kx^2+kx=x(k+1)+1+kx^2<=x(k+1)+1=1+(k+1)x

Answer 3

any question?

Answer 4

Thank you so much :) :) :)