MathCastle
Proof WritingHardInduction

Induction · Hard problem

A textbook states ∑i=1ni⋅2i=(n−1)2n+1+c\displaystyle \sum_{i=1}^{n} i\cdot2^i = (n - 1)2^{n+1} + c and proves it by induction. Use the base case n=1n = 1 to find cc.