to prove `(2^n+2^(n-1))/(2^(n+1)-2^n))=3/2` `(3^(-3)*6^2*sqrt98)/(5^2*(1/(25))^(1/3)*(15)^(-4/3)*3^(1/3))=28sqrt2`

Prove that: (3^(-3)x6^(2)x sqrt(98))/(5^(2)x(1)/(25)3x(15)^(-(4)/(3))x3^((1)/(3)))=28sqrt(2)

Prove that: (3^(-3)\ xx\ 6^2xx\ sqrt(98))/(5^2\ xx\ root(3)(1/(25))\ xx\ (15)^(-4/3)\ xx\ 3^(1/3))=28sqrt(2)

Prove that ((2n+1)!)/(n!)=2^(n)[1.3.5.....(2n-1)*(2n+1)]

If n=12 m(m in N), prove that ^n C_0-(^n C_2)/((2+sqrt(3))^2)+(^n C_4)/((2+sqrt(3))^4)-(^n C_6)/((2+sqrt(3))^6)+= (-1)^m((2sqrt(2))/(1+sqrt(3)))^ndot

If n=12 m(m in N), prove that ^n C_0-(^n C_2)/((2+sqrt(3))^2)+(^n C_4)/((2+sqrt(3))^4)-(^n C_6)/((2+sqrt(3))^6)+ddot=((2sqrt(2))/(1+sqrt(3)))^ndot

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

(1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+.....+(n^(2))/ ((2n-1)(2n+1))=((n)(n+1))/((2(2n+1)))

Prove that 1*2+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)

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