Estimating error using comparison/limit comparison test

1. Apr 11, 2008

motornoob101

I am confused about the right formula for this. Is it

$$R_{n} \leq T_{n} \leq\int_{n+1}_{\infty}$$ or $$R_{n} \leq T_{n} \leq\int_{n}_{\infty}$$?

Say for example, I want to estimate the error in using the sum of the first 10 terms to approximate the sum of the series.

The textbook seems to use both methods (Use n for the p-series and n+1 for the geometric series)

(as seen in the examples here)