# Just (not) Binomial Theorem

$(1+x)^{1000}+2x(1+x)^{999}+3x^2(1+x)^{998}+\cdots+1001x^{1000}$

If the coefficient of $$x^{50}$$ in the above expression is in the form $$\dbinom{1002}{k}$$ and $$k<100$$, then find the positive integer $$k$$.

 Notation: $$\dbinom MN = \dfrac {M!}{N! (M-N)!}$$ denotes the binomial coefficient.

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