Solving Series w/ Remainder Estimate & Integral Test

[skyturnred]

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

Homework Statement

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

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

Homework Equations

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!

 

[Deveno]

Homework Statement

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

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

Homework Equations

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!

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

 

[skyturnred]

Thanks! Thats what Ill do!