# It asks use remainder estimate for integral test to find series accurate to 3 dec?

1. Feb 16, 2012

### skyturnred

It asks "use remainder estimate for integral test" to find series accurate to 3 dec?

1. The problem statement, all variables and given/known data

It says "Use the Remainder Estimate for the Integral Test to find the sum of the following series to three decimal places of accuracy."

$\sum^{\infty}_{n=1}$ $\frac{1}{n^{3}}$

2. Relevant equations

3. The attempt at a solution

OK, so my question is as follows. If it says "to 3 decimal places of accuracy," what am I finding exactly? Am I finding the sum for error<0.001? or is it error<0.0005? I ask this because an error of 0.0005 could change the round and change the third decimal place.

As for the rest of the question, I know how to do it.

Thanks!

2. Feb 16, 2012

### Deveno

Re: It asks "use remainder estimate for integral test" to find series accurate to 3 d

i have always used < 0.0005, just because of the possibility of "rounding error" changing the 3rd decimal place.

3. Feb 16, 2012

### skyturnred

Re: It asks "use remainder estimate for integral test" to find series accurate to 3 d

Thanks! Thats what Ill do!