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" (iv) "quad C(o)+(3)/(2)*C(1)+(9)/(3)*C...

" (iv) "quad C_(o)+(3)/(2)*C_(1)+(9)/(3)*C_(2)+(27)/(4)*C_(3)+cdots+(3^(n))/(n+1)C_(n)=(4^(n+1)-1)/(3(n+1))

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Prove that following C_(0)+(3)/(2).C_(1)+(9)/(3).C_(2)+(27)/(4).C_(3)+……+(3^(n))/(n+1).C_(n)=(4^(n+1)-1)/(3(n+1)).

Prove that following C_(0)+(3)/(2).C_(1)+(9)/(3).C_(2)+(27)/(4).C_(3)+……+(3^(n))/(n+1).C_(n)=(4^(n+1)-1)/(3(n+1)).

4C_(0)+(4^(2))/(2)*c_(1)+(4^(3))/(3)c_(2)+............+(4^(n+1))/(n+1)C_(n)=(5^(n+1)-1)/(n+1)

(C_(0))/(2)+(C_(1))/(3)+(C_(2))/(4)+(C_(3))/(5)+.......+(C_(n))/(n+2)=(1+n*2^(n+1))/((n+1)(n+2))

(C_(0))/(1*2)+(C_(1))/(2*3)+(C_(2))/(3*4)+...+(C_(n))/((n+1)(n+2))=

(C_(0))/(1.2)+(C_(1))/(2.3)+(C_(2))/(3.4)+......*(C_(n))/((n+1)(n+2))=

C_(0)+C_(1)+2*C_(2)(3)+3*C_(3)(3^(2))+4*C_(4)(3^(3))+.......+n*C_(n)3^(n-1)=

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + … + C_(n) x^(n) , Show that (2^(2))/(1*2) C_(0) + (2^(3))/(2*3) C_(1) + (2^(4))/(3*4)C_(2) + ...+ (2^(n+2)C_n)/((n+1)(n+2))= (3^(n+2))/((n+1)(n+2))

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + … + C_(n) x^(n) , Show that (2^(2))/(1*2) C_(0) + (2^(3))/(2*3) C_(1) + (2^(4))/(3*4)C_(2) + ...+ (2^(n+2)C_n)/((n+1)(n+2))= (3^(n+2)-2n-5)/((n+1)(n+2))

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + … + C_(n) x^(n) , Show that (2^(2))/(1*2) C_(0) + (2^(3))/(2*3) C_(1) + (2^(4))/(3*4)C_(2) + ...+ (2^(n+2)C_n)/((n+1)(n+2))= (3^(n+2)-2n-5)/((n+1)(n+2))