If `(2+sqrt(3))^n=I+f,` where `I` and `n` are positive integers and 0

if f(x)=(a-x^n)^(1/n), where a > 0 and n is a positive integer, then f(f(x))= (i) x^3 (ii) x^2 (iii) x (iv) -x

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

Show that int_0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integer and , 0<=vltpi

Prove that (a) (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer. (b) (1+isqrt(3))^n+(1-isqrt(3)^n=2^(n+1)cos((npi)/3) , where n is a positive integer

Evaluate int_(0)^(infty)(x^(n))/(n^(x)) dx, where n is a positive integer.

Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

Show that the middle term in the expansion of (1 + x)^(2n) is (1.3.5.........(2n - 1))/(n!)2^(n)x^(n) , where n is a positive integer.

If (4+sqrt(15))^n=I+f,w h r en is an odd natural number, I is an integer and 0