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Let , then statement is true for
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a
all n∈N
b
all n>1
c
all n>1 provided x≠0
d
none of these
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Correct option is C
For n=2,P(2):(1+x)2=1+2x+x2>1+2x,as x≠0.Assume thatP(k):(1+x)k>1+kx (1)for some k∈N,k>1As x>−1, multiplying both the sides of (1) by 1+x, we get(1+x)k+1>(1+kx)(1+x)=1+(k+1)x+kx2>1+(k+1)x ∵ kx2>0Thus, P(k+1) is true.By the principle of mathematical induction P(n) is true forall n>1 provided x≠0.Talk to our academic expert!
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