Question

what is the coefficient of x^r in the expansion of (1+x)^n?​

Answer 1

Answer:

The above expansion can be written as {(1+x)^(n+1)-1}/{(1+x)-1}

=>The Numerator is a binominal expansion with power (n+1) and Denominator is x .So for that expression to get the coefficient of x^r brings back the coefficient of x^(r+1) in the binomial expansion of (1+x)^(n+1),which is

(n+1)C(r+1).Ans…