Hence expand $$$\left[1+\left(x+x^{2}\right)\right]^{5}$$$ in ascending powers of $$$x$$$ up to and including the term in $$$x^{3}$$$, simplifying your answer. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_13 Year：2020 Question No：4(b)

Answer:

$1+5\left(x+x^{2}\right)+10\left(x+x^{2}\right)^{2}+10\left(x+x^{2}\right)^{3}+\ldots$ SOI
$1+5\left(x+x^{2}\right)+10\left(x^{2}+2 x^{3}+\ldots\right)+10\left(x^{3}+\ldots\right)+\ldots \quad$ SOI
$1+5 x+15 x^{2}+30 x^{3}+\ldots$

Knowledge points:

1.6.1 use the expansion of , where is a positive integer (Including the notations and n!) (Knowledge of the greatest term and properties of the coefficients are not required.)

Answer:

Knowledge points:

Solution:

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