a problem with functions of binomials.

A question with functions of binomial random variables.

Let aj be the generic coefficient of a Binomial with parameters n and
p.

Similarly, let bj be the generic coefficient of a Binomial with
parameters (n+1) and p.

Now, let t be a positive real number and define the function H(y) as
the integral from 0 to y of the CUMULATIVE of a Normal distribution
with mean m and variance s^2.

Note that for any strictly positive t

Sum from 0 to n of ajx(tj/n) = Sum from 0 to n+1 of bjx(tj/n+1)=tp.

Ideally, what I want to show is that for any strictly positive t

Sum from 0 to n of ajxH(tj/n) > Sum from 0 to n+1 of bjxH(tj/n+1)

Alternatively, it will suffice to show that the difference is never
zero.

I have done many numerical simulations and the result always comes up.
Can anybody help?

Thank you.

.

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