The coefficient of $x^{24}$ in the expansion of $(1 + 3 x + 6 x^{2} + 10 x^{3} + - - - - + \infty)^{2 / 3} =$

300

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250

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205

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Solution

The correct option is C 25
The above expression can be simplified as
$[(1 - x)^{- 3}]^{\frac{2}{3}}$
$= (1 - x)^{- 2}$
Therefore coefficient of $x^{24}$
$=^{r + n - 1} C_{r}$
$=^{24 + 2 - 1} C_{24}$
$=^{25} C_{24}$
$= 25$
Hence answer is option C

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