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`

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)+.......= (-1)^m((2sqrt(2))/(1+sqrt(3)))^ndot

If n=12m(m in N), prove that ^nC_(0)-(^nC_(2))/((2+sqrt(3))^(2))+(^nC_(4))/((2+sqrt(3))^(4))-(^nC_(6))/((2+sqrt(3))^(6))+...=((2sqrt(2))/(1+sqrt(3)))^(n)

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

For all n in N,1+(1)/(sqrt(2))+(1)/(sqrt(3))+(1)/(sqrt(4))++(1)/(sqrt(n))

Prove that ^n C_0 ^(2n)C_n- ^n C_1 ^(2n-2)C_n+ ^n C_2^(2n-4)C_n-=2^ndot

lim_(nto oo)[(sqrt(n+1)+sqrt(n+2)+...+sqrt(2)n)/(sqrt(n^(3)))]

lim_(n rarr oo)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))