Dear student (1-x)-1=1+x+x2+x3+ +xk+ (1-x)-2=1+2x+3x2+4x3+ +(r+1)xk+ (1-x)-3=1+3x+6x2+10x4+ +r+1(r+2)r!xk+ In general coefficient of xk in (1-x)-n is n+k-1Cn Regards

sir

Dear student

(1 - x)^{- 1} = 1 + x + x^{2} + x^{3} + . . . . + x^{k} + . . . . (1 - x)^{- 2} = 1 + 2 x + 3 x^{2} + 4 x^{3} + . . . + (r + 1) x^{k} + . . . (1 - x)^{- 3} = 1 + 3 x + 6 x^{2} + 10 x^{4} + . . . . + \frac{(r + 1) (r + 2)}{r!} x^{k} + . . . . In general coefficient of x^{k} in (1 - x)^{- n} is^{n + k - 1} C_{n}

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