Question

is {n/((n+1)!)} n=1, infinity, monotone?

Answer 1

Are you talking about the limit, as n goes toward infinity, of n / (n+1)! ?

If so, then the limit is 0. If you think about it, you can factor that out as 1 / ( (n+1) * (n-1)!). The divisor gets very large, which means that the number gets gets increasingly closer to zero. It's monotone... since it's always decreasing towards zero.

Answer 2

The question states "Is the following sequence monotone? Justify your answer analytically." {n/(n+1)!} from n=1 to infinity.