Growing

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Seriesly

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Factorial Fun

How many divisors does factorial n (n!) have?

Weekly Challenge 36: Seriesly

Stage: 5 Short Challenge Level:
When proving an identity it is usually best to start with the more complicated expression and simplify it so this time start with the expression on the right hand side $(k+1)! - k!$. The algebra is easy.