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

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

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If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+C_(3).x^(3)+......+C_(n).x^(n), then prove that C_(0)+2C_(1)+4C_(2)+6C_(3)+...+2n.C_(n)=1+n*2^(n)

(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_(3).x^(3)+......+C_(n).x^(n), then prove that C_(0)+2C_(1)+4C_(2)+6C_(3)+…….+2n.C_(n)=1+n.2^(n)

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

Prove that C_(0)2^(2)C_(1)+3C_(2)4^(2)C_(3)+...+(-1)^(n)(n+1)^(2)C_(n)=0 where C_(r)=nC_(r)

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r), show that (C_(0))/(2)+(C_(1))/(3)+(C_(2))/(4)+...+(C_(n))/(n+2)=(n*2^(n+1)+1)/((n+1)(n+2))

If (1+x+x^(2))^(n)=(C_(0)+C_(1)x+C_(2)x^(2)+.........) then the value of C_(0)C_(1)-C_(1)C_(2)+C_(2)C_(3)...

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) prove that (C_(0))/(1) + (C_(2))/(3) + (C_(4))/(5) + ...= (2^(n))/(n+1) .

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