/sci/ - Science & Math

BROS HOW DO I KEEP GETTING THIS ONE WRONG?
The correct answer is supposedly D but I can't get it right for some odd reason.
Here's what I did:
1) Got the series for the integral
2) Replaced it with the integral
3) Integrated each one
4) Evaluated each one (I just skipped this one because of the 0 lower bound)
5) Plugged in 0.5 to the first 4 terms, found out that the 4th term satisfies the <10^-3 inequality
6) Added the first 3 terms that had been evaluated at 0.5, get 0.4604166 which is not on the answer list.
What's going on bros, pls, it's raping my head.