Prove that (1) `8C_0 + 8C_1 + 8C_2+...+8C_8 = 256`.: (2) `9C_0+ 9C_2+ 9C_4+......+9C_8 = 256`

Show that C_0 + C_1 + C_2 +...+ C_8 = 256

C_(0) + C_(1) + C_(2) +….. C_(8) = 256

Prove that ""^8C_5+""^8C_4=""^9C_5

Verify that : "^8C_4+ ^8C_3= ^9C_4 .

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 .

"^13C_9 - "^12C_8 =

Prove that , .^15C_8+.^15C_9-.^15C_6-.^15C_7=0

Show that: C_0 + C_2 + C_4 + C_6 + C_8 + C_10 = C_1 + C_3 + C_5 + C_7 + C_9 = 512

^8C_2+ ^8C_3+ ^8C_4+.... ^8C_7 is equal to

The value of (^8C_1+^8C_2+^8C_3+....+^8C_8) is