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" 18) "J(f)C(g(0))^(k)=^(16)C(gamma+2),"...

" 18) "J_(f)C_(g_(0))^(k)=^(16)C_(gamma+2)," find "^(8)C_(4)

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If ^(16)C_(r)=^(16)C_(r+2),f in d^(r)C_(4)

The value of (""^(47)C_(4))/(""^(57)C_(4))+sum_(j=0)^(3)(""^(50-j)C_(3))/(""^(57)C_(53))+sum_(j=0)^(5)""^((56-k)C_(53-k))/(""^(57)C_(4)) is :

The value of (""^(47)C_(4))/(""^(57)C_(4))+sum_(j=0)^(3)(""^(50-j)C_(3))/(""^(57)C_(53))+sum_(j=0)^(5)""^((56-k)C_(53-k))/(""^(57)C_(4)) is :

Find the sum sum_(j=0)^(n) (""^(4n+1)C_(j)+""^(4n+1)C_(2n-j)) .

Evaluate ^(47)C_(4)+sum_(j=0)^(3)""^(50-j)C_(3)+sum_(k=0)^(5) ""^(56-k)C_(53-k) .

Evaluate (47)C_(4)+sum_(j=0)^(3)""^(50-j)C_(3)+sum_(k=0)^(5) ""^(56-k)C_(53-k) .

Evaluate ^(47)C_(4)+sum_(j=0)^(3)""^(50-j)C_(3)+sum_(k=0)^(5) ""^(56-k)C_(53-k) .

If for z as real or complex . (1+z^(2) + z^(4))^(8) = C_(0) C_(1) z^(2) C_(2) z^(4) + …+ C_(16) z^(32) , prove that C_(0) + C_(3) + C_(6) + C_(9) + C_(12) + C_(15) + (C_(2) + C_(5) + C_(8) + C_(11) + C_(14)) + (C_(1) + C_(4) + C_(7) + C_(10) + C_(16)) omega^(2) = 0 , where omega is a cube root of unity .

Calculate the standard Gibbs energy change for the formation of propane at 298 K: 3C("graphite") + 4H_(2)(g) to C_(3)H_(8)(g) Delta_(f)H^(@) for propane, C_(3)H_(8)(g) = -103.8 kJ mol^(-1) . Given : S_(m)^(0)[C_(3)H_(8)(g)] = 270.2 J K^(-1) "mol"^(-1) S_(m)^(@)("graphite") = 5.70 J K^(-1) "mol"^(-1) and S_(m)^(0)[H_(2)(g)] = 130.7 J K^(-1) "mol"^(-1) .