Prove that: `(i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2` `(ii)\ (2^n+\ 2^(n-1))/(2^(n+1)-2^n)=3/2`

Prove that: sqrt((1)/(4))+(0.01)^(-(1)/(2))-(27)^((2)/(3))=(3)/(2) (ii) (2^(n)+2^(n-1))/(2^(n+1)-2^(n))=(3)/(2)

Prove that C_(0)-(1)/(3)*C_(1)+(1)/(5)*C_(2) - …+(-1)^(n)*(1)/(2n+1)C_(n) =(2^(2n)(n !)^(2))/((2n+1)!)

((-1+i sqrt(3))/(2))^(3 n)+((-1-i sqrt(3))/(2))^(3 n)=

Prove that : 1^(3)+2^(3)+3^(3)++n^(3)={(n(n+1))/(2)}^(2)

Prove that ((2n)!) / (n!) = 2^n(2n - 1) (2n - 3) ... 5.3.1.

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

Prove that ((2n+1)!)/(n!)=2^(n){1.3.5(2n-1)(2n+1)}

Prove that : 1^(2)+2^(2)+3^(2)+...+n^(2)=(n(n+1)(2n+1))/(6)

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