Thread: Detrmine whthere the sequence converges

An = 2((n+1)!) + 4^n / 2(n!)n^2

1) determine whether it converges and if it does, find the limit of the sequence {An}

I realise that i need to find the dominant term of the sequnece and to divide by this and so on, but i have not seen an example where (n+1)! is an element of the sequence and this has thrown me. Any help would be highly appreciated!! Limits is not my forte!

Originally Posted by raggie29

An = 2((n+1)!) + 4^n / 2(n!)n^2

1) determine whether it converges and if it does, find the limit of the sequence {An}

Which is it

The first one. Thanks.

Originally Posted by raggie29

The first one. Thanks.

Why don't you bother to use grouping symbols?
The way you posted the expression, it actually reads as the second one.



What can you say about

It is of form of a basic null sequence and hence = 0?

Originally Posted by raggie29

It is of form of a basic null sequence and hence = 0?

So what is the overall answer?

3/2n ??

Or is it, = 0? since 1/n and 1/n^2 are both basic null sequences?