General Binomial Expansion - Multiple (Edexcel A-Level Mathematics): Quizzes

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General Binomial Expansion - Multiple
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For what values of nn does the general binomial expansion of (1+x)n(1 + x)^n apply?

Any real number

For what range of xx does (1+x)n(1 + x)^n converge when nn is not a positive integer?

∣x∣<1|x| < 1

When nn is not a positive integer, what type of series is (1+x)n(1 + x)^n?

Infinite series

What is the coefficient of x2x^2 in (1+x)n(1 + x)^n using general binomial expansion?

n(n−1)2!\frac{n(n-1)}{2!}

What is the generalized binomial coefficient (nk)\binom{n}{k} for any real nn?

n(n−1)…(n−k+1)k!\frac{n(n-1)\dots(n-k+1)}{k!}

For small values of xx, how can the binomial series be used effectively?

Truncated for approximations

How are expressions like (a+b+c)n(a + b + c)^n with multiple terms typically handled?

Repeated application of binomial theorem

What is the coefficient of xx in the expansion of (1+x)12(1 + x)^{\frac{1}{2}}?

12\frac{1}{2}

First step to expand (2−3x)12(2 - 3x)^{\frac{1}{2}} using general binomial expansion?

Factor out 2122^{\frac{1}{2}}

For positive integer nn, what is the binomial coefficient (nk)\binom{n}{k}?

n!k!(n−k)!\frac{n!}{k!(n-k)!}

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