The co-efficient of $x^{n}$ in $(1 + x + 2 x^{2} + 3 x^{3} + . . . . . + n x^{n})$ is?

n

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\frac{n (n^{2} + 10)}{6}

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\frac{n (n^{2} + 11)}{4}

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\frac{n (n^{2} + 10)}{4}

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Solution

The correct option is A $n$
As we can see the expansion is :
$S = (1 + x + 2 x^{2} + 3 x^{3} + . . . . . . . . . . . . . + n x^{n})$

By simple observation, the coefficient of $n^{t h}$ term is $n$ (as given in the question itself)

Hence option (A) is the correct answer.

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