The number of terms in the expansion of $(1 + 2 x + x^{2})^{20}$ is:

21

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40

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20

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41

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Solution

The correct option is D $41$
Given
$(1 + 2 x + x^{2})^{20}$ $= (1 + x)^{40}$
General term given expansion
$T_{r + 1} = \sum_{r = 0}^{40}^{40} C_{r} x^{r}$
Hence the term from $0$ to $40$ is $41$

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