We can calculate the charge on #"Eu"# in each compound.
1) #"EuSO"_4#
#stackrelcolor(blue)("+2")("Eu")stackrelcolor(blue)("-2")("SO"_4)#
#"SO"_4"# has a charge of 2-, so #"Eu"# must have a charge of 2+.
2) #"Eu"_2("SO"_4)_3#
#stackrelcolor(blue)("+3")("Eu")_2stackrelcolor(blue)("-2")(("SO"_4)_3#
The three #"SO"_4^"2-"# ions have a total charge of 6-, so the two #"Eu"# ions must have a total charge of 6+.
One #"Eu"# ion must have a charge of 3+.
3) #"Eu""PO"_4#
#stackrelcolor(blue)("+3")("Eu")stackrelcolor(blue)("-3")("PO"_4)#
#"PO"_4"# has a charge of 3-, so #"Eu"# must have a charge of 3+.
4) #"Eu""(NO"_3)_3#
#stackrelcolor(blue)("+3")("Eu")stackrelcolor(blue)("-1")(("NO"_3))_3#
The three #"NO"_3"# ions have a total charge of 3-, so the #"Eu"# ion must have a charge of 3+.
One #"Eu"# ion must have a charge of 3+.
5) #"Eu""HCO"_3#
#stackrelcolor(blue)("+1")("Eu")stackrelcolor(blue)("-1")("HCO"_3)#
#"HCO"_3"# has a charge of 1-, so #"Eu"# must have a charge of 1+.
A charge of 1+ on #"Eu"# is not allowed.
The correct formulas are #"Eu"("HCO"_3)_2# and #"Eu"("HCO"_3)_3#