prove that : (1+x)(to power n ) > 1+nx ; for n>1 , x >-1

Asked by shuchi.saumya | 25th Sep, 2010, 12:00: AM

Expert Answer:

1+xn>1+nxProve by Mathematical inductionFor n=1, 1+x1=1+xAsume the result for n =k,1+xk>1+kx -----------(1)T.P.T the reult is true for n = k+1,i.e T.P.T 1+xk+1>1+(k+1)xNow 1+xk+1=1+xk1+x                            >(1+kx)(1+x)          by (1)                            = 1+(k+1)x+kx2>1+(k+1)x as kx2>0                             Hence proved by induction">

Answered by  | 25th Sep, 2010, 09:55: AM

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