Question Detail
Question
Find an expression in terms of n for the coefficient of x in \((1 + 4x) + (1 + 4x)^2 + \ldots + (1 + 4x)^n\).
Correct Answer
Option D is the correct answer.
Detailed Explanation
In each term (1+4x)^k, the coefficient of x is k·4. Summing from k=1 to n: Σ 4k = 4·n(n+1)/2 = 2n(n+1).
Hint
The coefficient of x in (1+4x)^k is 4k. Then sum over k.