How do you find the term independents in a binomial expansion?

3 viewed last edited 6 months ago

Anonymous

0

I know what the binomial expansion of a given expression is, but how do i find the term that is independent of x without using any generalised formulae?

Vivekanand Vellanki (last edited 6 months ago) (Expert, Founder @Qalaxia)

0

Not sure if I understood the question.

For an expression like \left(x+a\right)^n, the term independent of x is ^nC_0\cdot a^n because this represent the case where x is chosen 0 times.

For an expression like \left(x+\frac{1}{x}\right)^{2n}, the term independent of x is when x is chosen n times. Hence, the term independent of x is ^{2n}C_n\cdot x^n\cdot\left(\frac{1}{x}\right)^n