Quick Question about Sequence Notation

Question

If $b_n = \frac{1}{2n+1}$ does the notation $b_{n+1}$ make $b_n = \frac{1}{2(n+1)+1}$ or $b_n = \frac{1}{2n+2}$?

What does this have to do with sum notation? – Qiaochu Yuan Jan 20 '11 at 03:34 — Qiaochu Yuan, Jan 20 '11 at 03:34

score 4 · Accepted Answer · answered Jan 20 '11 at 02:03

4

The former: $b_{n+1} = \frac{1}{2(n+1)+1}$.

answered Jan 20 '11 at 02:03

NebulousReveal

13,935

score 4 · Answer 2 · answered Jan 20 '11 at 03:42

Ask yourself what you are replacing with $n+1$ to get $b_{n+1}$? You are replacing $n$, right? Therefore you also replace $n$ with $n+1$ in the expression on the right hand side of the equation. This gives $b_{n+1} = \frac{1}{2(n+1)+1}$ as PEV said.

Quick Question about Sequence Notation

2 Answers2