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Mathematics 29 Online
OpenStudy (anonymous):

Let x > -1 and n being a natural number Proove: (1+x)^n ≥ 1+nx

OpenStudy (anonymous):

Using induction

myininaya (myininaya):

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

myininaya (myininaya):

any question?

OpenStudy (anonymous):

Thank you so much :) :) :)

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