Use the sum of residues to find the unknown residues in the following expansions: (a) (F_{1}(s)=frac{600 s^{2}}{(s+10)(s+20)(s+30)}=frac{300}{s+10}+frac{k}{s+20}+frac{2700}{s+30})

Question:

Use the sum of residues to find the unknown residues in the following expansions:

(a) $F_{1}(s)=\frac{600 s^{2}}{(s+10)(s+20)(s+30)}=\frac{300}{s+10}+\frac{k}{s+20}+\frac{2700}{s+30}$

(b) $F_{2}(s)=\frac{20(s+10)}{(s+15)(s+20)}=\frac{k}{s+15}+\frac{40}{s+20}$

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