What is the significance of Ivan's relationship with Gerasim?

As Ivan's servant, he's not significant. As the one person in the novel who genuinely cares for Ivan, and who helps him ine every possible way, just because he's a GOOD man.......there's his significance.

"Gerasim did it all easily, willingly, simply, and with a good nature that touched Ivan Ilych. Health, strength, and vitality in other people were offensive to him, but Gerasim's strength and vitality did not mortify but soothed him." (7.32)

"Once when Ivan Ilych was sending him away he even said straight out: "We shall all of us die, so why should I grudge a little trouble?" – expressing the fact that he did not think his work burdensome, because he was doing it for a dying man and hoped someone would do the same for him when his time came." (7.33)

The significance of Ivan's relationship with Gerasim is the he is the complete opposite of Ivan. Ivan is, in the beginning of the novel, self-important, and cares only of what society thinks of him; he currently has no thoughs of death. Gerasim, on the other hand, acknolodges death, and does not ignore it. What really seems to draw Ivan to Gerasim is the fact that he seems to be the only one to pity him, instead of trying to ignore him.

Ivan then begins to learn from Gerasim; he learns to accept death. What first started out as a significant relationship, Ivan begins to lood at Gerasim as a teacher.