Question

sum(5n^n/n!) as n -> infinity

Answer 1

not much chance of that
the terms get larger, not smaller

Answer 2

how do you prove it using the limit test?

Answer 3

Geometric sequences: Determine whether the following sequences converge or diverge & describe whether they do so monotonically or by oscillation. {0.2^n}

Answer 4

limit test just says if \(\lim_{n\to \infty}a_n\neq 0\) then the sum does not converge

Answer 5

okay thanks

Answer 6

is it clear that the terms do not go to zero?

Answer 7

if not try it with say \(n=5\) and see what you have exactly
\[\frac{5\times 5\times 5\times 5\times 5}{5\times 4\times 3\times 2\times 1}\]\[=\frac{5}{4}\times \frac{5}{3}\times \frac{5}{2}\times 5\] so in fact this grow rather fast, faster than \(n\)

Answer 8

right okay i was a little confused on proving that lim n→∞ an≠0