Two-Decimal Place Accuracy: Sum & Integral Solution

[s3a]

Homework Statement

The problem along with its detailed solution are attached.

Homework Equations

Inequality, infinite summation and improper integral.

The Attempt at a Solution

I'm following the solution but I can't justify the first (and only) less-than-or-equal sign. Why is that sum less-than-or-equal to that integral?

Also, to be picky, when they say two-decimal place accuracy, shouldn't that mean error <= 5/10^3 instead of error < 5/10^3? Whether I am right or wrong, please tell me why.

Any input would be greatly appreciated!
Thanks in advance!

 

[Dick]

The sum is a lower Riemann sum for the area represented by the integral. Draw a picture that shows why. The picky bit is just to guarantee you don't get an answer like 0.025 and round off the wrong way. It's much less important than the first point.