Question

$(\frac{n}{0})+2(\frac{n}{1})+2^2(\frac{n}{2})+.....+2^n(\frac{n}{n})$ is equal to.

• A. $2^n$
• B. $0$
• C. $3^n$
• D. None of these

Answer 1

The correct option is C $3^n$

We know that the expansion of $(x+1{)}^n$ is

$=(\frac{n}{0})+x(\frac{n}{1})+x^2(\frac{n}{2})+\cdots +x^n(\frac{n}{n})$

If we put $x=2$ in the above equation then,

$(2+1{)}^n=(\frac{n}{0})+2(\frac{n}{1})+\cdots +2^n(\frac{n}{n})=3^n$