First slide
Introduction to P.M.I

Let x>1, then statement P(n):(1+x)n>1+nx is true for


For n=2,

P(2):(1+x)2=1+2x+x2>1+2x,as x0.

Assume that

P(k):(1+x)k>1+kx                            (1)

for some kN,k>1

As x>1, multiplying both the sides of (1) by 1+x, we get



Thus, P(k+1) is true.

By the principle of mathematical induction P(n) is true for
all n>1 provided x0.

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