Suppose k is a binomial random variable with parameters n and p and let x=(k-np)//sqrt(npq) where q=1-p. If x is of o(n^(1//6)) and there exist some positive numbers A,B and C then show that |(b(k;n,p)sqrt(npq))/(varphi(x))-1| < (A)/(n)+(B|x|^(3))/(sqrtn)+(C|x|)/(sqrtn), where b(k;n,p) is probability mass function of a binomial random variable and varphi(x) is the probability density function of a normal random variable.

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