" Show that "C_(0)+C_(1)+C_(2)+......+C_(8)=256

Show that C_(0) + C_(1) + C_(2) + …. + C_(10) = 1024

Prove that (1)8C_(0)+8C_(1)+8C_(2)+...+8C_(8)=256...(2)9C_(0)+9C_(2)+9C_(4)+......+9C_(8)=256

" 0.Show that "C_(0)-4.C_(1)+7.C_(2)-10.C_(3)+.....=0

Show that: C_(0) + C_(2) + C_(4) +…… + C_(12) = C_(1) + C_(2) + C_(3) + C_(5) + ……. + C_(11) = 2048

Show that C_0 + C_1 + C_2 +...+ C_9 = 512

Show that: C_0 + C_1 + C_2 +..........+ C_10 = 1024

Show that C_(1)+C_(2)+C_(3)+...+C_(n)=1+2+2^(2)+...+2^(n-1)

If (1+x)^(n) = C_(0)+C_(1).x+C_(2). x^(2)+..+C_(n). x^(n) then C_(0)+2. C_(1)+3. C_(2)+..+(n+1). C_(n) =

Show that C_(0) +(C_(0) +C_(1))+(C_(0)+C_(1)+C_(2)) +…+(C_(0) +C_(1)+…+C_(n)) =(n+2).2^(n-1)

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 .