Answer: Based on your description, in which you mention it is some but not all of the tips turning brown, I suspect it may be setting spores on the brown tips. You should cut these off as you do not want it to spread beyond the window box. New growth will come up from the roots to hide the cut ends.
This plant does best in evenly moist soil. In hot summer weather it can be difficult to keep the soil evenly moist. You may need to water daily, especially if the container is relatively small compared to the top growth of the plant. Check the soil with your finger to see if you need to water more often.
Other than a little watering, this plant is very easy to grow. Please keep it in a container and do not plant it in the ground -- in the ground it can quickly become invasive and is very difficult to eradicate.
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