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Find the coefficients of x^(50) in the e...

Find the coefficients of `x^(50)` in the expression `(1+x)^(1000)+2x(1+x)^(999)+3x^2(1+x)^(998)+....+1001 x^(1000)` .

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To find the coefficient of \( x^{50} \) in the expression \[ (1+x)^{1000} + 2x(1+x)^{999} + 3x^2(1+x)^{998} + \ldots + 1001x^{1000}, \] we can denote this entire expression as \( S \). ...
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