यदि `(1+x)^(n)=C_(0)+C_(1)x+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n)`, तो सिद्ध कीजिए कि -
(i) `C_(0)+2C_(1)+3C_(2)+...+(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))/(lfloorn)`