Algebra

$2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.$

We can calculate that $2 \cdot 2^2$is 8, and that $3 \cdot 2^3$ is 24, and because 8 + 24 is 32, then n is 3, and the equation $2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32$ is $2 \cdot 2^2 + 3 \cdot 2^3 =32$

Answer: 3