Question

verify that each equation is true for every positive integer n. 1(1!) + 2(2!) + ⋯ + n(n!) = (n + 1)! – 1

Answer 1

so whats our strategy?

Answer 2

where should we begin our proof?

Answer 3

\[\sum_{k=1}^{n}k\cdot k! \]\[= \sum_{k=1}^{n}(\overline{k+1} - 1) \cdot k!\]