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Previous Year Question (PYQs)
1
In the expression
$(x+1)(x+4)(x+9)(x+16)\cdots(x+400)$
the coefficient of $x^{19}$ is
Solution
Coefficient of $x^{19}$ equals sum of constants:
$1+4+9+\cdots+400$
This is sum of squares from $1^2$ to $20^2$:
$\frac{20(21)(41)}{6}=2870$
Answer: $\boxed{2870}$
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