Write and simplify, in terms of $n$, the first four terms in the expansion of $(1 + 2x)^n$ in as

Question

Write and simplify, in terms of $n$, the first four terms in the expansion of $(1 + 2x)^n$ in ascending powers of $x$.[3] Given that the ratio of the coefficient of $x^2$ to that of $x^3$ in the expansion of $(1 + 2x)^n$ is $3 : 20$, find the value of $n$ where $n$ is a positive integer.[3]

Accepted Answer

(a) $1+2nx+2n(n-1)x^2+\dfrac43n(n-1)(n-2)x^3+\cdots$ (b) $n=12$

2023 CSS AM S3 EOY Q10

2023 CSS AM S3 EOY Q10

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