+1859 Compute the unique positive integer $n$ such that
2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.
+289 \(2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.\)
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
