1. convergence of sequence

Give an example of a sequence (an) such that an>5 for all n belongs to $\displaystyle N$ with (an) converging to 5.

I'm asked to not only give example,but also need to write detailed explanation,please help me,I don't know how to do it.Thanks a lot.

2. Originally Posted by tsang
Give an example of a sequence (an) such that an>5 for all n belongs to $\displaystyle N$ with (an) converging to 5.
We are not supposed to knowingly help you with homework or anything else that counts towards a grade. However, I'd like you to clarify what "n belongs to $\displaystyle N$" means. Does it mean that $\displaystyle a_n$ is an integer for all n?

3. Originally Posted by Vlasev
We are not supposed to knowingly help you with homework or anything else that counts towards a grade. However, I'd like you to clarify what "n belongs to $\displaystyle N$" means. Does it mean that $\displaystyle a_n$ is an integer for all n?
sorry that I just didn't know the code for the symbol, "n belongs to N" just to say that a1,a2,a3,a4....
Also, it is just my homework practice, I'm a very honest person, it is only for homework practice, nothing will count towards grade of course.
I simply just started Real Analysis study,and so I asked teacher for a lot questions for me to practice,I simply call it homework.

4. Hi,
for example : $\displaystyle a_n=5+\frac{1}{n}$