I would most certainly take sharp scissors or pruners and cut the damaged fronds off right at the soil line.
What type of water do you have? The yellowing tips indicate high salts in the soil. Some of our tap water is full of salts and toxins. Did you transplant this guy after purchasing or is this his original pot and soil from the nursery?
If you haven't watered for 3 weeks...that is a bit too long but your palm still looks healthy, the soil has probably become hydrophobic and repels water.
I would put this plant into your shower, turn the cold water on and let it rain and rain and rain for 5 minutes. Stick something under the pot lifting off the bottom of the shower or tub and allow it to drain for an hour or so. Give it a shake now and then to get rid of the water on the leaves. Make sure to lift the pot and plant to feel what it feels like when it is properly watered.* *Do not water it again until you lift it and it is very light. Then water thoroughly.
The shower thing is great every 3 months or so to wash off dust and leach salts from the soil. Take it back to its normal spot. Put pieces of broken 1/4" tile beneath the pot to lift it off of the surface of the saucer. This greatly enhances drainage. The longer water sits in your soil, fungus amungus can get started and/or the roots won't be able to get air. Roots need O2. Or they start drowning/rotting.
You will have to transplant this palm, sooner than later. Get a pot that is just a few inches larger than this pot, clay pot, wider than tall. I would use a 14" wide by 12" deep clay pot.
Use plain potting soil without any water holding gimmicks or fertilizer added. Don't add a single thing to that soil. Fill 1/3, FIRM, place your plant into the new soil and lightly open up the outside circling roots and as you add soil lightly firm.
Your goal is to make sure the surface of the soil and the crown of your plant end up 1" from the rim of your pot...for proper watering.
Ask those guys at the nursery when the last time it was fertilized and with WHAT. Be nice to know that information, but if impossible, purchase a small bottle of OSMOCOTE, `14-14-14, extended release and use HALF of what the directions tell you. This will last you and this plant for years.
Keep your plant in the spot it is in now. It looks great for light and no drafts?
When you do the up potting/transplanting, turn your plant on its side to slide the root ball out of the pot (on newspaper), if there are roots coming out of the drain holes, cut them off. If the plant and its root ball doesn't slide out easily...WHACK the side of the pot. If that doesn't work WHACK it again...the side of the pot as it lays on the newspaper, even a third or fourth time?
It will slide out then look at those roots. Are they bright white or do you see brown and/or mushy roots? Take a picture and send it with another question. Use ONLY sterilized potting soil, the plainer and cheaper the better.
The rock on top of the soil doesn't need to be there. Let us know how this works out!