Question

how can this limit be solved???


limit (x->infinit) (
3^x)/(1*2*3....*x)

Answer 1

This will go to zero.

Answer 2

yes, I know it will go to zero, but is there an easy way to solve it (I ahve found a long long one)

Answer 3

You can say that every time x increases by 1, you are multiplying the numerator by 3 and multiplying the denominator by a bigger number.
So as x goes to infinity, you keep multiplying the numerator by 3 while multiplying the denominator by infinity (essentially)

Answer 4

ok, is this right?

f(x)=3^x/x!
for x>3 -> f(x+1)=f(x)*3/x < f(x+1)

Answer 5

anything / a very large number = 0.

Answer 6

that's the simplest answer.