If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+â€¦.+C_(n).x^(n). then prove that (i) C_(0)+2C_(1)+3C_(2)+â€¦+(n-1)C_(n)=(n+2).2^(n-1) (ii)C_(0)+3C_(1)+5C_(2)+...+(2n+1)C_(n)=(n+1).2^(n) (iii)C_(0)+(C_(2))/(3)+(C_(4))/(5) +....+(2^(n))/(n+1) (iv) 2C_(0)+(2^(2).C_(1))/(2) +(2^(3).C_(2))/(3)+...+(2^(n+1).C_(n))/(n+1) =(3^(n+1)-1)/(n+1) (v) (C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))......(C_(n-1)+C_(n)) =(C_(1)C_(2)C_(3)........C_(n)(n+1)^(n))/(|uln)

If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+â€¦.+C_(n).x^(n). then prov

1.	If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+â€¦.+C_(n).x^(n). then prove that (i) C_(0)+2C_(1)+3C_(2)+â€¦+(n-1)C_(n)=(n+2).2^(n-1) (ii)C_(0)+3C_(1)+5C_(2)+...+(2n+1)C_(n)=(n+1).2^(n) (iii)C_(0)+(C_(2))/(3)+(C_(4))/(5) +....+(2^(n))/(n+1) (iv) 2C_(0)+(2^(2).C_(1))/(2) +(2^(3).C_(2))/(3)+...+(2^(n+1).C_(n))/(n+1) =(3^(n+1)-1)/(n+1) (v) (C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))......(C_(n-1)+C_(n)) =(C_(1)C_(2)C_(3)........C_(n)(n+1)^(n))/(\|uln)
Answer» SOLUTION :N/a