Prove that : If n is a positive integer, then prove that
`C_(0)+(C_(1))/(2)+(C_(2))/(3)+….+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1).`

Prove that : If n is a positive integer then prove that i) C_(0)+C_(1)+C_(2)+……+C_(n)=2^(n)

C_0-(C_1)/(2)+(C_2)/(3)-…...+(-1)^n (C_n)/(n+1)=

Prove the following: C_(0)-(C_(1))/(2)+(C_(2))/(3) - …+(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

Prove that : If n is a positive integer and x is any nonzero real number, then prove that C_(0)+C_(1)(x)/(2)+C_(2).(x^(2))/(3)+C_(3).(x^(3))/(4)+….+C_(n).(x^(n))/(n+1)=((1+x)^(n+1)-1)/((n+1)x)

Prove that (C_1)/(2) + (C_3)/(4) + (C_5)/(6) + (C_7)/(8) + …… = (2^n - 1)/(n+ 1)

If n is a positive integer, prove that sum_(r=1)^(n)r^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

Prove that following (C_(1))/(2)+(C_(3))/(4)+(C_(5))/(6)+(C_(7))/(8)+……=(2^(n)-1)/(n+1)

Prove that (C_0)/(1)+ (C_2)/(3) + (C_4)/(5) + (C_6)/(7) +…….= (2^n)/(n+ 1)

Prove the following: C_(0)+(C_(2))/(3) +(C_(4))/(5) + … = (2^(n))/(n+1)

If n is a positive integer prove that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos((n pi)/(2))