## kimmy0394 Group Title Suppose {an} is a sequence that converges to a number L > 0. What is the limit of {an + 1}? one year ago one year ago

1. KingGeorge Group Title

Since it converges, you have that for all $$\epsilon>0$$, $$|L-a_n|<\epsilon$$ for all $$n>N$$ for some $$N\in\mathbb{N}$$. Now, we guess that $$\{a_n+1\}$$ converges to $$L+1$$. Look at $$|L+1-(a_n+1)|$$. What can you say about it?

2. kimmy0394 Group Title

It's a with subscript (n+1) . I'm ask confused with your symbols

3. KingGeorge Group Title

Ah. So your new sequence is $$\{a_{n+1}\}$$?

4. kimmy0394 Group Title

Yes

5. terenzreignz Group Title

Hey, @kimmy0394 When you think about it $\huge a_{n+1}$is just the same sequence, just that it starts one step ahead of $\huge a_n$ right?

6. kimmy0394 Group Title

right!