What is the formula for the sum: #1+2*2+3*3*3+4*4*4*4+...+overbrace(n*n*n*...*n)^"n terms"# ?
1 Answer
Sep 6, 2017
Explanation:
There is no nice algebraic closed formula for this sum.
About the best we can do is provide some notation...
#1+2 * 2+3 * 3 * 3+4 * 4 * 4 * 4+...+overbrace(n * n * n * ... * n)^"n times" = sum_(k=1)^n k^k#
and note that:
#lim_(n->oo) (sum_(k=1)^n k^k)/n^n = 1#