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

Prove that: C_(1) + 2C_(2) + 3C_(3) + 4C_(4) +….. + nC_(n) = n.2^(n-1)

C_(1) + C_(2) + C_(3) + ….. C_(n) = 2^(n)-1

Show that: C_1/C_0 + 2 C_2/C_1 + 3 C_3/C_2 + .... + n C_n/(C_n -1) = (n(n+1))/2

Show that C_0 + 2C_1 + 3C_2 +4C_3 +...+ (n + 1)C_n = (n + 2)2^(n-1)

Show that C_1 + C_2 + C_3 +...+ C_n = 2^n - 1

Prove the following by the method of induction for all n in N : 1^2 + 3^2 + 5^2 + ... + (2n - 1)^2 = n/3 (2n -1) (2n +1)

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

By method of induction prove that 1.3 + 2.5 + 3.7 +...+ n (2n + 1) = n/6 (n + 1) (4n + 5) for all n in N

Prove the following by the method of induction for all n in N : 1/1.3 + 1/3.5 + 1/5.7+...+ 1 / ((2n-1)(2n+1)) = n / (2n+1)

Prove the following by the method of induction for all n in N : 1.2 + 2.3 + 3.4 +...+ n(n + 1) = n/3 (n+1)(n+2).