# Neglect terms of order $1/n$

I have expressions like the following $$A+B/n+C/n^2+\cdots,Z/n^p$$. I'd like to keep just the first two terms, i.e., $$A+B/n,$$ however it seems that using the command O[1/n^2] is not working. The O[] command used to neglect higher-order terms seems to work only for expressions like $$A+B n+C n^2+\cdots,Z n^p.$$ Is there any workaround to deal with expressions like mine?

## 1 Answer

Given:

expr = a + b/n + c/n^2 + d/n^3;


Use either:

expr + O[n, Infinity]^2 //TeXForm


$$a+\frac{b}{n}+O\left(\left(\frac{1}{n}\right)^2\right)$$

or:

Series[expr, {n, Infinity, 1}] //TeXForm


$$a+\frac{b}{n}+O\left(\left(\frac{1}{n}\right)^2\right)$$