Find the coefficient of x ^ 3 in (x + 1) + (1 + x) ^ 2 +. + (1 + x) ^ 10 expansion

Sum (x + 1) + (1 + x) ^ 2 +. + (1 + x) ^ 10 by equal ratio sequence
[(1+x)-(1+x)^10]/(-x).
Therefore, we only need to find the coefficient of x ^ 4 in (1 + x) ^ 10
From the general term formula of binomial, C (10) 4 = 210,
So the coefficient of x ^ 3 in the expansion is 210

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