Question:

Let $f(x)=\sum_{k=1}^{10}kx^k$. If $2f(2)+f'(2)=2^n\cdot m+1$ with $m$ odd, then $n$ is equal to

Step-by-Step Solution

Key Concept: $f(x)=\frac{x(1-x^{10})}{(1-x)^2}-\frac{10x^{11}}{1-x}$. Compute $f(2)$ and $f'(2)$.

$n=10$.

Correct Answer: 10