kindness to the family
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I actually was not to sure about the history between Hrothgar and Ecgtheow. Check the following excerpt out. I'll list it in the source link below. Hope it helps.
Hrothgar came to know Beowulf’s father when he was a young boy. He was friends with Beowulf’s father, Ecgtheow. He says that he has heard tales of Beowulf’s great prowess and one time Hrothgar recounts a feud during which Beowulf’s father killed Heatholaf, a member of the Wulfing tribe. Hrothgar sent treasure to the Wulfings to mend the feud, and Beowulf’s father pledged his allegiance to Hrothgar. I think that Beowulf does feel indebted to Hrothgar for his past kindnesses to the family because when Beowulf’s father killed Heatholaf, it could have led to a huge war and it could have hurt the Danes, but Hrothgar stopped that from happening. He did Ecgtheow a HUGE favor and I think Beowulf should do Hrothgar the HUGE favor of killing Grendel.