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

Prove that following C_(0)-4.C_(1)+7.C_(2)-10.C_(3)+……=0, if n is an even positive integer.

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

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0)+4C_(1)+8C_(2)+12C_(3)+......+4nC_(n)=1+n.2^(n+1)

If C_(0)+C_(1)+C_(2)+......+C_(n)=128 then C_(0)-(C_(1))/(2)+(C_(2))/(3)-(C_(3))/(4)+.....=

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

If C_(0)+C_(1)+C_(2)+......+C_(n)=128 then C_(0)-(C_(1))/(2)+(C_(2))/(3)-(C_(3))/(4)+......=

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : 3.^(n)C_(0)-8.^(n)C_(1)+13.^(n)C_(2)-18.^(n)C_(3)+....."up to"(n+1)"terms" =0